anonymous
  • anonymous
Simplify the following complex fractions Please help algebra questions
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1377646677230:dw|
phi
  • phi
multiply top and bottom by 1/3 as a first step you get \[ \frac{1}{3}\left(\frac{1}{x+1}+ \frac{1}{x}\right)\] you can add the two fractions by using a common denominator of x(x+1)
anonymous
  • anonymous
ok then what

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phi
  • phi
can you add the fractions ?
anonymous
  • anonymous
2/x3|dw:1377648290193:dw|
phi
  • phi
oh, wait... you want to subtract the two fractions \[ \frac{1}{3}\left(\frac{1}{(x+1)}\frac{x}{x}- \frac{1}{x}\frac{(x+1)}{(x+1)}\right) \]
anonymous
  • anonymous
ok so from the start again step by step what do i do
phi
  • phi
multiply top and bottom by 1/3. the bottom 3*1/3 becomes 1 \[ \frac{ \frac{1}{3}\cdot\left(\frac{1}{x+1}+ \frac{1}{x}\right)}{3\cdot \frac{1}{3}} \] that becomes \[ \frac{1}{3}\cdot\left(\frac{1}{x+1}+ \frac{1}{x}\right)\] now multiply the first fraction by x/x and the second fraction by (x+1)/(x+1)
anonymous
  • anonymous
is that for subtraction
phi
  • phi
you get \[ \frac{1}{3}\left(\frac{1}{(x+1)}\frac{x}{x}- \frac{1}{x}\frac{(x+1)}{(x+1)}\right) \] the fractions become \[ \frac{1}{3}\left(\frac{x - (x+1)}{x(x+1)} \right)\]
phi
  • phi
*yes it should be subtraction.
anonymous
  • anonymous
ok now what would u do
anonymous
  • anonymous
now
phi
  • phi
simplify the top x - (x+1) that is the same as x + -1*(x+1) you "distribute" the -1 by multiplying each term inside the parens by -1 can you do that ?
anonymous
  • anonymous
i dont know how to do that
phi
  • phi
you don't know how to multiply -1 * (x+1) ? multiplying each term inside the parens by -1 means put -1* in front of the x and in front of the 1 what do you get ?
anonymous
  • anonymous
-x+1
phi
  • phi
how about -1*x + -1*1 now simplify that. -1*x is -x and -1*1 is ?
anonymous
  • anonymous
-x-1
anonymous
  • anonymous
how would that look all together now
phi
  • phi
so now you have in the top x - (x+1) becomes x -x -1 what is 1 x take away 1 x ?
anonymous
  • anonymous
0
anonymous
  • anonymous
|dw:1377649248129:dw|
phi
  • phi
so x -x -1 is just -1
phi
  • phi
so the top is -1 the bottom stays the same, it is x(x+1)
anonymous
  • anonymous
ok now the next step would be the bottom
phi
  • phi
we can't do much with the bottom the answer is \[ - \frac{1}{3x(x+1)} \]
anonymous
  • anonymous
ok and is there a way to double check that so in the future I can make sure i got it right
anonymous
  • anonymous
is that the most it can go
phi
  • phi
you could use wolfram to check your answers for this problem you can distribute the 3x(x+1) in the bottom to get 3x^2 +3x but normally you would leave it the way we have it now.
anonymous
  • anonymous
how would i put it in on wolfram
anonymous
  • anonymous
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anonymous
  • anonymous
can u help with the others

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