Question

Please help I’m struggling on this question.

Answer 1

Answer:
`(2(y^2-4y+40))/((y-8)(y+4))`

Explanation:

To solve this problem, we want to make sure the denominators are the same on both fractions. Once they are equal, we can dd them together.

`(y+4)/(y-8) +(y-8)/(y+4)` [multiply first fraction by y+4 and second by y-8]

`((y+4)(y+4))/((y-8)(y+4)) +((y-8)(y-8))/((y-8)(y+4))` [distribute by FOIL]

`(y^2+8y+16)/((y-8)(y+4)) +(y^2-16y+64)/((y-8)(y+4))` [add numerator]

`(y^2+8y+16+y^2-16y+64)/((y-8)(y+4))` [combine like terms]

`(2y^2-8y+80)/((y-8)(y+4))` [factor out 2 from numerator]

`(2(y^2-4y+40))/((y-8)(y+4))`

Now we know that
`(2(y^2-4y+40))/((y-8)(y+4))` is the factored form after adding.