Question

How do you divide `\frac { 10x ^ { 2} + 35x } { 18x ^ { 3} - 12x ^ { 2} } \div \frac { 4x ^ { 2} + 14x } { 6x ^ { 2} - 4x }`?

Answer 1

`5/(6x)`

Explanation:

`(10x^2+35x)/(18x^3-12x^2)divide (4x^2+14x)/(6x^2-4x)`

Simplify
`10x^2+35x=5x(2x+7)`
`18x^3-12x^2=6x^2(3x-2)`
`4x^2+14x=2x(2x+7)`
`6x^2-4x=2x(3x-2)`

=`(5x(2x+7))/(6x^2(3x-2))times(2x(3x-2))/(2x(2x+7))`

Cancel out the common factors
=`(5cancelxcancel(2x+7))/(6x^cancel2cancel(3x-2))times(cancel(2x(3x-2))/cancel(2x(2x+7)))`

=`5/(6x)`