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

Question

1523 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-18T17:41:50

$(x-2)/x$

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

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:

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

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

$(x-2)/x$

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