How do you multiply and simplify #\frac{ 4( y - 2) }{ x } \cdot \frac{ 3x }{ 6( y - 2) ^ { 2} }#?

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Answer 1 · 2017-01-03T13:33:33

See full simplification process steps below:

First, multiply the numerator and the denominator separately like you would when multiplying any fractions:

#(4(y - 2) xx 3x)/(x xx 6(y - 2)^2)#

Next, expand the exponent terms in the denominator:

#(4color(blue)((y - 2)) xx 3color(red)(x))/(color(red)(x) xx 6color(blue)((y - 2))(y - 2))#

The cancel the like terms in the numerator and denominator:

#(4cancel(color(blue)((y - 2))) xx 3cancel(color(red)(x)))/(cancel(color(red)(x)) xx 6cancel(color(blue)((y - 2)))(y - 2))#

#(4 xx 3)/(6(y-2))#

Now multiply out the numerator and simplify with the constant in the denominator:

#color(red)(12)/(color(red)(6)(y - 2)#

#2/(y-2)#