Answer:
The friend's answer is incorrect.
The correct answer is:
[tex] \dfrac{3(x - 1)}{x + 2} [/tex]
Step-by-step explanation:
[tex] \dfrac{x^2 - 1}{x^2 - 4x - 5} \div \dfrac{2x^2 + 4x}{6x^2 - 30x} = [/tex]
To divide by a fraction, multiply by its reciprocal.
[tex] = \dfrac{x^2 - 1}{x^2 - 4x - 5} \times \dfrac{6x^2 - 30x}{2x^2 + 4x} [/tex]
Multiply the numerators together. Multiply the denominators together.
[tex] = \dfrac{(x^2 - 1)(6x^2 - 30x)}{(x^2 - 4x - 5)(2x^2 + 4x)} [/tex]
Factor every polynomial.
[tex] = \dfrac{(x - 1)(x + 1)(6x)(x - 5)}{(x - 5)(x + 1)(2x)(x + 2)} [/tex]
Divide the numerator and denominator by the common terms.
[tex] = \dfrac{(x - 1)(6)}{(2)(x + 2)} [/tex]
[tex] = \dfrac{3(x - 1)}{x + 2} [/tex]
The friend's answer is incorrect.
The correct answer is:
[tex] \dfrac{3(x - 1)}{x + 2} [/tex]
