How would you solve x-4/x+5 = x^2-x-12/?

Question

i'm supposed to solve for the question mark (?).

and the two fractions are supposed to be set equal to each other.

Answer 1

first factor out the x^2 -x-12.

the factors are (x-4)(x+3)

rewrite the equation: (x-4) / (x+5) = (x-4)(x+3) / ?

both sides has a (x-4) so we can cancel them out:

1/(x+5) = (x+3)/?

now cross multiply:

? = (x+5)(x+3)

you could leave it like that or multiply it out:

? = x^2 +8x+15

Answer 2

first factor x^2-x-12 to (x-4)(x+3)

(x-4)/(x+5)=((x-4)(x+3))/?

(x-4)(x+3)/((x+5)(x+3))=((x-4)(x+3))/?

(x+5)(x+3)=?

x^2+8x+15=?

make it a good day