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

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Answer 1 · 2016-11-20T13:49:07

#1/(2y)#

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)#