I have to add by using a common denominator. 12 over x^2+5x-24+3/x-3

Question

The answer had to be in simplest form. Please help ASAP

Answer 1

x²+5x-24=(x+8)(x-3), so:

12/[(x+8)(x-3)]+3/(x-3)=(3/(x-3))(4/(x+8)+1)= (the common factor 3/(x-3) is factored out to simplify the working)

(3/(x-3))(4+x+8)/(x+8)= (4/(x+8)+1 is the same as 4/(x+8)+(x+8)/(x+8), so we can combine the two numerators: 4+x+8 and place them over the common denominator x+8)

(3/(x-3))(x+12)/(x+8)= (the numerator 4+x+8 can be simplified by adding the numbers: x+12)

3(x+12)/[(x+8)(x-3)] or (3x+36)/(x²+5x-24). (Note how the numerators and denominators are combined.)