anonymous
  • anonymous
simplify complex fractions:
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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amistre64
  • amistre64
complex as in with the imaginary "i"?
anonymous
  • anonymous
all you need to know is i^2 = -1
anonymous
  • anonymous
no mutiplying and dividing rational expressions \[(x^3y^2z)/(a^2b^2)/(a^3x^2y)/(b^2)\]

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anonymous
  • anonymous
where the slash is its written like a fraction
anonymous
  • anonymous
So what is over what here?
anonymous
  • anonymous
stack the parenthisis up ontop of each other where it looks like a fraction with things. idk how to punch it in on here were it looks like it does on my worksheet
amistre64
  • amistre64
you can use // to mean the main divider bar between them, or some other version like */* just explain the symbol :)
anonymous
  • anonymous
From what it looks like, I would assume it's like a rational expression over another. Correct?
amistre64
  • amistre64
the b^2.s cancel out
anonymous
  • anonymous
yes rational expressions
amistre64
  • amistre64
basic strategy as with all fraction on fraction math is to turn the bottom one upside down and multiply across... 1/5 // 6/3 = 1/5 * 3/6 = 3/30
anonymous
  • anonymous
but when its all letters and exponets how do you do it
amistre64
  • amistre64
you mean the multiply part? or the flipping part?
anonymous
  • anonymous
the multiply part. flipping i get now but idk what to do with the letters
amistre64
  • amistre64
make it easier on yourself and split them up... a^4 means aaaa c^2 mean cc r^7 means rrrrrrr
amistre64
  • amistre64
now, x^3 times x^4 means xxx xxxx = xxxxxxx = x^7
amistre64
  • amistre64
c^4 times c^5 means cccc ccccc = ccccccccc = c^9
anonymous
  • anonymous
yea i get the x^4 means xxxx but what about x^3y^2z
amistre64
  • amistre64
xxx yy z is all that is
amistre64
  • amistre64
squish em all together, then count them back out again....
anonymous
  • anonymous
what your confusing me
anonymous
  • anonymous
a/x = a* 1/x, therefore \[(x ^{3}y ^{2}z)/(a ^{2}b ^{2})/(a ^{2} x ^{2} y)/(b ^{2})] = \[(x ^{3} y ^{2} z)/(a ^{2} b2) * 1/(a ^{2} x ^{2} y)/(b ^{2})] = \[(x ^{3} y ^{2} z)/(a ^{2} b ^{2})*(b^{2})/(a ^{2} x ^{2} y)\]
amistre64
  • amistre64
xxx yy z bb -------- x ------ aa bb aaa xx y
amistre64
  • amistre64
anything that is the same on the top and bottom can be tossed out, it just means it equals 1. x y z 1 x y z xyz ----- x ---- = ------ = ---- aa aaa aaaaa a^5
anonymous
  • anonymous
still not makin a whole lota sense
amistre64
  • amistre64
which part is not making sense?
amistre64
  • amistre64
i flipped it, you said thatpart you understood.... whats left?
amistre64
  • amistre64
Does: xx y bb ------ = 1? xx y bb
anonymous
  • anonymous
the whole thing. its a fraction placed ontop on a fraction saying simplify. like am i supposed to add the exponets together, flip them and multiply, or flip and divide
amistre64
  • amistre64
flip the bottom, thats always the first step. split the exponents up so you can see what you got whatever is the same from top to bottom cancels out to 1 squish the rest together and number them again with an exponent.
amistre64
  • amistre64
lets keep it simpler, how would I start this? x^2/y^3 // y/x^2
anonymous
  • anonymous
flip it and take away the x^2 and just leave it as xy^3/xy i think
amistre64
  • amistre64
one step at a time, dont rush ahead... lets flip the bottom x^2 x^2 ---- * ---- now what do I do? y^3 y
anonymous
  • anonymous
the x^2 ---- y part
anonymous
  • anonymous
oh wait y^3 x y ------- x^2 x^2
amistre64
  • amistre64
you let me worry about making it look good on the screen, just tell me what we do next...
amistre64
  • amistre64
I already flipped it, x^2 x^2 ---- * ---- now what do I do? y^3 y
anonymous
  • anonymous
i want to say crossmultiply
anonymous
  • anonymous
but thats usually not with letter
amistre64
  • amistre64
we do that if there is an (=) between them, there is no (=) here so we dont "cross" multilply, we just multiply straight across
anonymous
  • anonymous
ok just add the exponets together
amistre64
  • amistre64
-------------->> x^2 x^2 x^2 x^2 ---- * ---- = ---------- y^3 y y^3 y -------------->> does this look right to you?
anonymous
  • anonymous
not really shouldnt it be x^3/y^4
amistre64
  • amistre64
not yet.... but does the setup look right? did I multiply it across correctly?
anonymous
  • anonymous
yea i think.
amistre64
  • amistre64
now lets add exponents to get the final result x^2 x^2 x^(2+2) x^4 ------- = --------- = ---- y^2 y y^(2+1) y^4
amistre64
  • amistre64
2+1 = 3... sorry, forgot how to add :)
anonymous
  • anonymous
that looks more like it
amistre64
  • amistre64
so lets try your original problem and see if we can step thru it ok?
anonymous
  • anonymous
ok
amistre64
  • amistre64
x^3 y^2 z --------- a^2 b^2 --------------- a^3 x^2 y -------- b^2 our first step is to do what?
anonymous
  • anonymous
im working it on a sheet of paper and the first thing i did was put the bottom fraction beside it and put a division sign between them
amistre64
  • amistre64
ok.... x^3 y^2 z a^3 x^2 y --------- / ---------- a^2 b^2 b^2 now what?
anonymous
  • anonymous
um flip the entire thing upside down or add the exponets
amistre64
  • amistre64
only flip the right side fraction... not the "whole" problem....JUST that right side gets flipped. right?
anonymous
  • anonymous
ok
amistre64
  • amistre64
just like this.... x^3 y^2 z b^2 --------- ---------- a^2 b^2 a^3 x^2 y
anonymous
  • anonymous
yea then add the exponets together
amistre64
  • amistre64
what do you mean by add the exponents together? that is not really something that needs to be done just yet. Look at the top and the bottom of this oversized fraction and see if we can cross out stuff that looks the same.
amistre64
  • amistre64
lets "line" things up from top to bottom....are we allowed to do that?
anonymous
  • anonymous
line things up idk what your talking about
amistre64
  • amistre64
I am going to move the stuff around so that it looks better. Like this..... x^3 y^2 z b^2 -------------------- x^2 y a^2 a^3 b^2
amistre64
  • amistre64
what can you see that we can "get rid of" that is the same from the top and the bottom?
anonymous
  • anonymous
um on the bottom combine the a^2 and a^3 together to get a^5
amistre64
  • amistre64
good we can do that... x^3 y^2 z b^2 -------------------- x^2 y a^5 b^2
anonymous
  • anonymous
can we also combine the x^3 and x^2 or not since there on seperate parts of the equation
amistre64
  • amistre64
we cant "add" them together but watch this: xx x ---- = what? xx
anonymous
  • anonymous
5
amistre64
  • amistre64
no....not quite. do you remember that anything when placed over itself is equal to 1? 2 -- = 1 2 6m --- = 1 6m xx -- = 1 xx
anonymous
  • anonymous
i think
amistre64
  • amistre64
this is a fundamental concept in math. whenever we "divide" a number by itself we get an answer of 1 1 --- 8 | 8 right?
anonymous
  • anonymous
i guess but i dont particularly see how that would work in this type of problem
amistre64
  • amistre64
all fractions are is division. what is 1 divided by 2 = 1/2 3 divided by 5 = 3/5 15 divided by 5 = 15/5 all fractions are division......
amistre64
  • amistre64
when we divide a number by itself we get 1 9 divided by 9 = 9/9 = 1
anonymous
  • anonymous
but in this case were dividing x^3/ x^2
amistre64
  • amistre64
exactly :) which is why I like to split it up so that you can "see" what is going on with exponents. x x x xx x ---- = --- -- = 1x = x x x xx 1
anonymous
  • anonymous
so like that i can just "get rid of" the x part in the equation
amistre64
  • amistre64
not the whole thing... but you can get rid of alot of x s how many x's do I have left in my solution up there?
anonymous
  • anonymous
the x^3 and the x^2 so 5 i think
amistre64
  • amistre64
x x x xx x ---- = --- -- = 1x = x x x xx 1 ^ how many x's do I have right here?
anonymous
  • anonymous
1
amistre64
  • amistre64
then we are left with 1 lonely little x that we have to leave in this equation.... right?
anonymous
  • anonymous
yea
amistre64
  • amistre64
you know already that we we multiply exponents we "add" then together. When we do the opposite of multiplication (which is division) we do the opposite to the exponents too. we "SUBTRACT them. x^3/x^2 = x^(3-2) = x^1 = x
anonymous
  • anonymous
ok so how do we plug this one lonely x into the equation
amistre64
  • amistre64
we just put it back were we got it from :) like this: x y^2 z b^2 ------------- y a^5 b^2
anonymous
  • anonymous
ok what next. same thing to the b^2s
amistre64
  • amistre64
yep, that would be good. b^2/b^2 is division.... so we SUBTRACT exponents. b^(2-2) = b^0 = 1 which just disappears
anonymous
  • anonymous
ok so the b is just slapped onto the end of the top part of the equation without the exponent on it
amistre64
  • amistre64
there is no b to put back if b^3 means bbb and b^1 means b b^0 means _______ no little b's to do anything with, zero b's, they are gone......
anonymous
  • anonymous
so on the actual equation after this last part the b will be no more
amistre64
  • amistre64
thats correct, they vanished...... x y^2 z --------- now whats left to work with? y a^5
anonymous
  • anonymous
the y
amistre64
  • amistre64
very good :) so, can you show me how we work that out?
anonymous
  • anonymous
y^2/y^19(which is just nothing) subtract them and it leaves y
amistre64
  • amistre64
perfect!!
amistre64
  • amistre64
x y z ------ we appear to have come to the end :) a^5
anonymous
  • anonymous
that 9 wasnt supposed to be there my finger sliped off the shift button when i hit the paraenthasis
amistre64
  • amistre64
i figured that :)
anonymous
  • anonymous
weird stinkin keyboards
amistre64
  • amistre64
i start getting so many typos it looks like im having a stroke......
anonymous
  • anonymous
back during the first of march i was in germany on a school junior senior trip and their keyboard was all kinds of weird
amistre64
  • amistre64
Yep different places have different setups for their own uses. But this is the answer to our original problem.... x y z ------ a^5
amistre64
  • amistre64
I just want to go over one little detail.....
anonymous
  • anonymous
ok
amistre64
  • amistre64
when dividing with exponents, it is important to notice where the biggest one is. For example: x^3/x^2 has the bigger number on top, so our answer goes back on top. BUT if the bottom has the bigger exponent, our answer will go back on the bottom. for example: x^2/x^7 has the bottom bigger than the top, we subtract like before but when were done our leftovers go on the bottom. Does that make sense?
anonymous
  • anonymous
yea location of the bigger exponet is where the outcome of the division goes
amistre64
  • amistre64
very good :) Ciao
anonymous
  • anonymous
thank you so much if i have anymore questions ill just post them up and maybe be able to catch ya

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