Multiply the rational expression and write the product in the simplest form: (x^(2)+2x-3)/(x^(2)+3x-4)+(x^(2)+6x+8)/(x^(2)-9)

Answer 1

To multiply the rational expression, we must first factorize the denominators:

Denominator 1: x^2 + 3x - 4 = (x + 4)(x - 1)
Denominator 2: x^2 - 9 = (x + 3)(x - 3)

Therefore, the expression becomes:

[(x^2 + 2x - 3)/(x + 4)(x - 1)] * [(x^2 + 6x + 8)/(x + 3)(x - 3)]

Next, we multiply the numerators and denominators:

[(x^2 + 2x - 3)(x^2 + 6x + 8)] / [(x + 4)(x - 1)(x + 3)(x - 3)]

Expanding the numerators:

[(x^4 + 8x^3 + 22x^2 + 16x - 24)] / [(x + 4)(x - 1)(x + 3)(x - 3)]

Simplifying the expression further is not possible in this case.