Question

Divide and simplify.

Answer 1

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Answer 2

First thing is to remember that when you are dividing rational expressions, you change the sign to multiplication and flip the second expression.\[\frac{ 3x ^{3} }{ 4y }\times \frac{ 9y }{ x }\]Now you can cancel stuff out, top to bottom (never top to top or bottom to bottom). The x in the denominator of the second expression cancels with the x^3 in the numerator of the first expression leaving nothing in the denominator of the second and reducing the numerator in the first by x to leave x^2. Now do the same with the y's. They both cancel out completely, so here's what we have left to work with:\[\frac{ 3x ^{2} }{ 4 }\times \frac{ 9 }{ 1 }\]Multiply straight across the top and the bottom to get a final reduced expression of \[\frac{ 27x ^{2} }{ 4 }\]