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

`\large\boxed{(x+3)/(x^2-x-12)\cdot(x-4)/(x^2-8x+16)=(1)/(x^2-8x+16)}`

Explanation:

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