Question

How do you multiply `\frac{x^{2} + 9x + 20}{x^{2} + x - 20} \cdot \frac{x^{2} - 25}{x^{2} - x - 20}`?

Answer 1

`(x+5)/(x-4)`

Explanation:

In algebraic fractions, factorize, factorize, factorize!
`\frac{x^{2} + 9x + 20}{x^{2} + x - 20} \cdot \frac{x^{2} - 25}{x^{2} - x - 20}`

=`((x+4)(x+5))/((x+5)(x-4) )xx ((x+5)(x-5))/((x-5)(x+4)`

Now cancel like factors at top and bottom.

`(cancel(x+4)cancel(x+5))/(cancel(x+5)(x-4) )xx ((x+5)cancel(x-5))/(cancel(x-5)cancel(x+4)`

`(x+5)/(x-4)`