anonymous
  • anonymous
Combine as indicated by the signs: 4/y^2-9 + 5/y+3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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UsukiDoll
  • UsukiDoll
do you know how to factor? and take the least common denominator?
anonymous
  • anonymous
...unfortunatly i dont really I'm in the process of teaching myself.
UsukiDoll
  • UsukiDoll
\[\frac{4}{y^2-9} + \frac{5}{y+3}\]

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UsukiDoll
  • UsukiDoll
there is a perfect square for the first fraction in the denominator ... a product of some integer with itself. \[y^2-9\]
UsukiDoll
  • UsukiDoll
in the form of \[(a^2-b^2) =(a+b)(a-b)\] so if we let a = y^2 and b=9 we need to take the square root of y^2 and the square root of 9. Can you do that?
anonymous
  • anonymous
wouldnt the square root of y^2 just be y and the square root of 9 is 3?
UsukiDoll
  • UsukiDoll
yay!
UsukiDoll
  • UsukiDoll
so since we have a = y and b = 3 we have \[(y^2-9)=(y+3)(y-3) \]
UsukiDoll
  • UsukiDoll
\[\frac{4}{(y+3)(y-3)} + \frac{5}{y+3}\]
UsukiDoll
  • UsukiDoll
now noticed how our denominators are different? :O we need to take the lcd.. since lcd is (y+3)(y-3) we need to multiply ?????????????? so the denominator in the second fraction is the same as the denominator in the first fraction
UsukiDoll
  • UsukiDoll
so what is missing in the denominator for the second fraction? I have y+3 but I don't have ?????
anonymous
  • anonymous
y-3? im kinda lost.
UsukiDoll
  • UsukiDoll
you're on the right track
UsukiDoll
  • UsukiDoll
so we multiply y-3 on the numerator for the second fraction and multiply y-3 on the denominator for the second fraction as well
UsukiDoll
  • UsukiDoll
\[\frac{4}{(y+3)(y-3)} + \frac{5}{y+3} \times \frac{y-3}{y-3}\] your fraction will look something like this
UsukiDoll
  • UsukiDoll
\[\frac{4}{(y+3)(y-3)} + \frac{5(y-3)}{y+3(y-3)} \] so we distribute the 5 all over y-3
UsukiDoll
  • UsukiDoll
can you distribute the 5 towards y-3 ? it's like multiplying 5 times y and 5 times -3
anonymous
  • anonymous
5y-15?
UsukiDoll
  • UsukiDoll
\[\frac{4}{(y+3)(y-3)} + \frac{5y-15}{y+3(y-3)}\] yes
UsukiDoll
  • UsukiDoll
\[\frac{4+5y-15}{(y+3)(y-3)} \] now we need to compute 4-15
anonymous
  • anonymous
-11
UsukiDoll
  • UsukiDoll
correct
UsukiDoll
  • UsukiDoll
\[\frac{5y-11}{(y+3)(y-3)}\]
UsukiDoll
  • UsukiDoll
we can't factor anything out and there's nothing to cancel, so we're done
anonymous
  • anonymous
ok i got it and can you look at one more problem and tell me why my answer is only partially right?
UsukiDoll
  • UsukiDoll
sure
anonymous
  • anonymous
8-y/3y + y+2/9y - 2/6y i got 2y+23/9y
UsukiDoll
  • UsukiDoll
\[\frac{8-y}{3y}+ \frac{y+2}{9y}-\frac{2}{6y}\] this?
anonymous
  • anonymous
yes
UsukiDoll
  • UsukiDoll
ok so all of them have y in common but we notice that the denominators are different.. we also notice that the third fraction \[\frac{2}{6}\] can be reduced . can you reduce that fraction for me?
anonymous
  • anonymous
1/3
UsukiDoll
  • UsukiDoll
\[\frac{8-y}{3y}+ \frac{y+2}{9y}-\frac{1}{3y}\] alright... now we noticed that the first and third fraction has the same denominator, so we can rewrite this fraction and solve . \[\frac{8-y}{3y}-\frac{1}{3y}+ \frac{y+2}{9y}\] \[\frac{8-y-1}{3y}+\frac{y+2}{9y}\] can you combine like terms on the first fraction ?
UsukiDoll
  • UsukiDoll
we just have to do this arithmetic 8-y-1 which can be rewritten as -y+8-1
anonymous
  • anonymous
ok
anonymous
  • anonymous
?
UsukiDoll
  • UsukiDoll
so what is the answer?
UsukiDoll
  • UsukiDoll
I can't combine variables... but I can combine numbers for -y+8-1
anonymous
  • anonymous
so would it just be -1+8-1/9y?
UsukiDoll
  • UsukiDoll
no.. leave -y alone .. what is 8-1?
anonymous
  • anonymous
7
UsukiDoll
  • UsukiDoll
\[\frac{-y+7}{3y}+\frac{y+2}{9y}\] yes.. we still can't add these denominators.. we have the y's so we just need a number so 3 x ? = 9
anonymous
  • anonymous
3
UsukiDoll
  • UsukiDoll
\[\frac{3(-y+7)}{9y}+\frac{y+2}{9y}\]
UsukiDoll
  • UsukiDoll
now distribute the 3 what is 3 times -y what is 3 x 7 ?
anonymous
  • anonymous
3 x 7=21 3 x-y=-3y
UsukiDoll
  • UsukiDoll
\[\frac{(-3y+21)}{9y}+\frac{y+2}{9y}\]
UsukiDoll
  • UsukiDoll
so what is -3y+y what is 21+2
UsukiDoll
  • UsukiDoll
\[\frac{(-3y+y+21+2)}{9y}\]
anonymous
  • anonymous
23 and -4y
UsukiDoll
  • UsukiDoll
23 is correct but for the y portion that's wrong
UsukiDoll
  • UsukiDoll
if you're adding a big negative number and a small positive number, your answer should go down.
UsukiDoll
  • UsukiDoll
\[\frac{(-3y+y+23)}{9y}\]
UsukiDoll
  • UsukiDoll
try again what is -3y+y
UsukiDoll
  • UsukiDoll
hmmm... let's ignore the y part ... let's just solve -3+1 think of it as... you want to buy something for $3 but you only have $1, how much more do you need to buy that product?
anonymous
  • anonymous
2
UsukiDoll
  • UsukiDoll
yeah, but there's one problem... you're $2 in the red in that example, so -2 is the answer
UsukiDoll
  • UsukiDoll
\[\frac{(-2y+23)}{9y}\]
UsukiDoll
  • UsukiDoll
you had the correct answer but you forgot the - sign on the 2y.. I highly suggest you practice on adding and subtracting with negative numbers
anonymous
  • anonymous
i see now that makes more sense and i totally will work on it ha! thanks

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