7/w^2-9-x+4/w^2-6w-27

Question

dont get it.

Answer 1

7 / (w²-9) - (w+4) / (w²-6w-27)

 

(I'm assuming that x should be a w.)

 

 

First, factor the denominators:

 

7 / ((w-3)(w+3)) - (w+4) / ((w-9)(w+3))

 

Then multiply the first fraction by (w-9)/(w-9) and the second by (w-3)/(w-3) so they have a common denominator:

 

(7(w-9)) / ((w-3)(w+3)(w-9)) - ((w+4)(w-3)) / ((w-3)(w+3)(w-9))

 

Combine the fractions into one and foil the numerators:

 

(7(w-9) - (w+4)(w-3)) / ((w-3)(w+3)(w-9))

(7w - 63 - (w² -3w +4w -12)) / ((w-3)(w+3)(w-9))

(7w - 63 - w² + 3w - 4w + 12) / ((w-3)(w+3)(w-9))

 

Combine like terms in the numerator to find your final answer:

 

(-w² + 6w - 51) / ((w-3)(w+3)(w-9))