Question

Combine as indicated by the signs:
4/y^2-9 + 5/y+3

Answer 1

do you know how to factor? and take the least common denominator?

Answer 2

...unfortunatly i dont really I'm in the process of teaching myself.

Answer 3

\[\frac{4}{y^2-9} + \frac{5}{y+3}\]

Answer 4

there is a perfect square for the first fraction in the denominator ... a product of some integer with itself. \[y^2-9\]

Answer 5

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?

Answer 6

wouldnt the square root of y^2 just be y and the square root of 9 is 3?

Answer 7

yay!

Answer 8

so since we have a = y and b = 3 we have \[(y^2-9)=(y+3)(y-3) \]

Answer 9

\[\frac{4}{(y+3)(y-3)} + \frac{5}{y+3}\]

Answer 10

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

Answer 11

so what is missing in the denominator for the second fraction? I have y+3 but I don't have ?????

Answer 12

y-3? im kinda lost.

Answer 13

you're on the right track

Answer 14

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

Answer 15

\[\frac{4}{(y+3)(y-3)} + \frac{5}{y+3} \times \frac{y-3}{y-3}\] your fraction will look something like this

Answer 16

\[\frac{4}{(y+3)(y-3)} + \frac{5(y-3)}{y+3(y-3)} \]
so we distribute the 5 all over y-3

Answer 17

can you distribute the 5 towards y-3 ? it's like multiplying

5 times y and 5 times -3

Answer 18

5y-15?

Answer 19

\[\frac{4}{(y+3)(y-3)} + \frac{5y-15}{y+3(y-3)}\] yes

Answer 20

\[\frac{4+5y-15}{(y+3)(y-3)} \] now we need to compute 4-15

Answer 21

-11

Answer 22

correct

Answer 23

\[\frac{5y-11}{(y+3)(y-3)}\]

Answer 24

we can't factor anything out and there's nothing to cancel, so we're done

Answer 25

ok i got it and can you look at one more problem and tell me why my answer is only partially right?

Answer 26

sure

Answer 27

8-y/3y + y+2/9y - 2/6y

i got 2y+23/9y

Answer 28

\[\frac{8-y}{3y}+ \frac{y+2}{9y}-\frac{2}{6y}\] this?

Answer 29

yes

Answer 30

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?

Answer 31

1/3

Answer 32

\[\frac{8-y}{3y}+ \frac{y+2}{9y}-\frac{1}{3y}\] 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 ?

Answer 33

we just have to do this arithmetic

8-y-1 which can be rewritten as -y+8-1

Answer 34

ok

Answer 35

?

Answer 36

so what is the answer?

Answer 37

I can't combine variables... but I can combine numbers for
-y+8-1

Answer 38

so would it just be -1+8-1/9y?

Answer 39

no.. leave -y alone .. what is 8-1?

Answer 40

7

Answer 41

\[\frac{-y+7}{3y}+\frac{y+2}{9y}\] yes.. we still can't add these denominators.. we have the y's so we just need a number

so 3 x ? = 9

Answer 42

3

Answer 43

\[\frac{3(-y+7)}{9y}+\frac{y+2}{9y}\]

Answer 44

now distribute the 3

what is 3 times -y
what is 3 x 7 ?

Answer 45

3 x 7=21 3 x-y=-3y

Answer 46

\[\frac{(-3y+21)}{9y}+\frac{y+2}{9y}\]

Answer 47

so what is -3y+y
what is 21+2

Answer 48

\[\frac{(-3y+y+21+2)}{9y}\]

Answer 49

23 and -4y

Answer 50

23 is correct but for the y portion that's wrong

Answer 51

if you're adding a big negative number and a small positive number, your answer should go down.

Answer 52

\[\frac{(-3y+y+23)}{9y}\]

Answer 53

try again what is -3y+y

Answer 54

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?

Answer 55

2

Answer 56

yeah, but there's one problem... you're $2 in the red in that example, so
-2 is the answer

Answer 57

\[\frac{(-2y+23)}{9y}\]

Answer 58

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

Answer 59

i see now that makes more sense and i totally will work on it ha! thanks