I'm trying to improve my maths so I can sit the GRE this time next year.
I'm stuck on a really silly question:
Express as a single fraction:
$$\frac{\frac{3x}{2y-7y}}{4x}$$
I'm trying to find a common denominator to cancel out the bottom line. Am I on the right track?
Best Answer
Yes, you are on the right track, but in order to do that you will need to multiply up by the denominators, or their multiples, to get the lowest common denominator, I get $4xy$.
Multiply the left fraction by $\frac{2x}{2x}$ and the right fraction by $\frac{y}{y}$
$\frac{3x}{2y}(\frac{2x}{2x})-\frac{7y}{4x}(\frac{y}{y})=\frac{6x^2}{4xy}-\frac{7y^2}{4xy}=\frac{6x^2-7y^2}{4xy}$
As you have stated in the comments that the actual question is: $\frac{3x}{2y-\frac{7y}{4x}}$, if I have understood you correctly, I will answer that now:
$\frac{3x}{2y(\frac{4x}{4x})-\frac{7y}{4x}}=\frac{3x}{\frac{2y-5y}{4x}}=\frac{3x(4x)}{-5y}=\frac{-12x^2}{5y}$