Question

15. Change the fraction w – 3 / w + 5 into an equivalent fraction with the denominator w^2 + w – 20.

A.w^2 + 7w – 12 / w^2 + w – 20.


B.w^2 – 7 – 12 / w^2 + w – 20


C.w^2 – 7w + 12 / w^2 + w – 20


D.w^2 + 7w + 12 / w^2 + w – 20

Answer 1

w^2 + w - 20 = (w + 5)(w - 4)

(w - 3) (w - 4) w^2 - 7w + 12
---------- * -------- = ------------------
(w + 5) (w - 4) w^2 + w - 20

Answer 2

C.
`(w^2-7w+12)/(w^2+w-20)`

Explanation:

We have been given a fraction
`(w-3)/(w+5)` and we are asked to write the equivalent fraction of our given fraction with the denominator
`w^2+w-10`.

First of all we will divide
`w^2+w-10` by
`w+5` to find the expression that we need to multiply with our given fraction to get the denominator
`w^2+w-10`

Let us factor out
`w^2+w-10` by splitting the middle term

`w^2+w-10`

`w^2+5w-4w-20`

`w(w+5)-4(w+5)`

`(w+5)(w-4)`

`(w^2+w-20)/(w+5)=((w+5)(w-4))/((w+5))=(w-4)`

Now we will multiply the numerator and denominator of
`(w-3)/(w+5)` by
`(w-4)` to find the equivalent fraction.

`(w-3)/(w+5)*((w-4))/((w-4))`

`((w-3)*(w-4))/((w+5)*(w-4))`

`(w^2-4w-3w+12)/(w^2-4w+5w-20)`

`(w^2-7w+12)/(w^2+w-20)`

Therefore, option C is the correct choice.