Answer:
C. [tex]\frac{w^2-7w+12}{w^2+w-20}[/tex]
Step-by-step explanation:
We have been given a fraction [tex]\frac{w-3}{w+5}[/tex] and we are asked to write the equivalent fraction of our given fraction with the denominator [tex]w^2+w-10[/tex].
First of all we will divide [tex]w^2+w-10[/tex] by [tex]w+5[/tex] to find the expression that we need to multiply with our given fraction to get the denominator [tex]w^2+w-10[/tex]
Let us factor out [tex]w^2+w-10[/tex] by splitting the middle term
[tex]w^2+w-10[/tex]
[tex]w^2+5w-4w-20[/tex]
[tex]w(w+5)-4(w+5)[/tex]
[tex](w+5)(w-4)[/tex]
[tex]\frac{w^2+w-20}{w+5}=\frac{(w+5)(w-4)}{(w+5)}=(w-4)[/tex]
Now we will multiply the numerator and denominator of [tex]\frac{w-3}{w+5}[/tex] by [tex](w-4)[/tex] to find the equivalent fraction.
[tex]\frac{w-3}{w+5}*\frac{(w-4)}{(w-4)}[/tex]
[tex]\frac{(w-3)*(w-4)}{(w+5)*(w-4)}[/tex]
[tex]\frac{w^2-4w-3w+12}{w^2-4w+5w-20}[/tex]
[tex]\frac{w^2-7w+12}{w^2+w-20}[/tex]
Therefore, option C is the correct choice.
