Question

What is a simlified form of x+3 over x^2-x-12 multiplied by x-4 over x^2-8x+16?

Answer 1

Answer:

$\large\boxed{\dfrac{x+3}{x^2-x-12}\cdot\dfrac{x-4}{x^2-8x+16}=\dfrac{1}{x^2-8x+16}}$

Step-by-step explanation:

$\dfrac{x+3}{x^2-x-12}\cdot\dfrac{x-4}{x^2-8x+16}=\dfrac{x+3}{x^2+3x-4x-12}\cdot\dfrac{x-4}{x^2-8x+16}\\\\=\dfrac{x+3}{x(x+3)-4(x+3)}\cdot\dfrac{x-4}{x^2-8x+16}=\dfrac{x+3}{(x+3)(x-4)}\cdot\dfrac{x-4}{x^2-8x+16}\\\\\text{cancel}\ (x+3)\ \text{and}\ (x-4)\\\\=\dfrac{1}{x^2-8x+16}$