Question

How do you divide `\frac { x ^ { 2} - 4} { x ^ { 2} + 7x + 10} \div \frac { x } { x + 5}`?

Answer 1

`(x-2)/x`

Explanation:

`\frac { x ^ { 2} - 4} { x ^ { 2} + 7x + 10} \div \frac { x } { x + 5}`

is the same thing as inverting and multiplying:

`(x^2-4)/(x^2+7x+10) * (x+5)/x`

Now let's factor and see if we can remove some terms:

`((x-2)(x+2))/((x+5)(x+2)) * (x+5)/x`

`((x-2)cancel((x+2)))/(cancel((x+5))cancel((x+2))) * cancel((x+5))/x`

`(x-2)/x`