Question

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

Answer:

C. $\frac{w^2-7w+12}{w^2+w-20}$

Step-by-step explanation:

We have been given a fraction $\frac{w-3}{w+5}$ 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

$w^2+w-10$

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

$w(w+5)-4(w+5)$

$(w+5)(w-4)$

$\frac{w^2+w-20}{w+5}=\frac{(w+5)(w-4)}{(w+5)}=(w-4)$

Now we will multiply the numerator and denominator of $\frac{w-3}{w+5}$ by $(w-4)$ to find the equivalent fraction.

$\frac{w-3}{w+5}*\frac{(w-4)}{(w-4)}$

$\frac{(w-3)*(w-4)}{(w+5)*(w-4)}$

$\frac{w^2-4w-3w+12}{w^2-4w+5w-20}$

$\frac{w^2-7w+12}{w^2+w-20}$

Therefore, option C is the correct choice.