Mathematics: 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

15. change the fraction w – 3 / w + 5 into an equivalent

Ответ:

anna2894

08.01.2022

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

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.

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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

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