Question

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

Answer 1

`1/(2y)`

Explanation:

The first step with algebraic fractions is to factor wherever possible.

`(6x^2)/(4x^2y-12xy)div (3x^2 +12x)/(x^2+x-12)`

`"only one term"/("common factor") div "common factor"/"quadratic trinomial"`

`(6x^2)/(4xy(x-3))div (3x(x+4))/((x+4)(x-3))" "larr` multiply and invert

`(6x^2)/(4xy(x-3))xx ((x+4)(x-3))/(3x(x+4))" "larr`cancel like factors

`(cancel6^cancel2x^2)/(cancel4^2xycancel((x-3)))xx (cancel((x+4))(cancel(x-3)))/(cancel3x(cancel(x+4)))`

`x^2/(2x^2y)`

=`1/(2y)`