How do you multiply #\frac { x ^ { 2} - 4} { 12x } \cdot \frac { 3x } { x + 2}#?

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Answer 1 · 2016-11-21T22:34:36

#(x - 2)/4#

First we should factor the quadratic #x^2 - 4# or:

#x^2 + 0x - 4 => (x - 2)(x + 2)#

We can now multiply the numerator and denominator of the fractions:

#((x - 2) * (x + 2) * 3x)/(12x * (x + 2))#

We can regroup to:

#((x - 2)*(x + 2)*3x)/((x + 2)*12x) =>#

#((x - 2)*(x + 2)*3x)/((x + 2)*4*3x) =>#

#((x - 2)*cancel((x + 2))*cancel(3x))/(cancel((x + 2))*4*cancel(3x)) =>#

#(x - 2)/4#