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

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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#