Question

How do you simplify `frac{x^{2}+2x-80}{x^{2}-100}\cdot \frac{x^{2}-9x-10}{x^{2}-4x-32}`?

Answer 1

`"answer "(x+1)/(x+4)`

Explanation:

`(x^2+2x-80)/(x^2-100)*(x^2-9x-10)/(x^2-4x-32)`
`"Please remember the following mathematical identities."`

`x^2+2x-80=(x+10)(x-8)`
`x^2-100=x^2-10^2=(x-10)(x+10)`
`x^2-9x-10=(x-10)(x+1)`
`x^2-4x-32=(x-8)(x+4)`
`"let us write the equation again."`
`((x+10)(x-8))/((x-10)(x+10))*((x-10)(x+1))/((x-8)(x+4))`

`"let us simplify."`

`(cancel((x+10))cancel((x-8)))/(cancel((x+10))cancel((x-10)))*(cancel((x-10))(x+1))/(cancel((x-8))(x+4))`

`"we get;"`
`(x+1)/(x+4)`