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:


I'm trying to find a common denominator to cancel out the bottom line. Am I on the right track?

  • 3
    $\begingroup$ Yes you are on the right track $\endgroup$ – Astyx Oct 30 '16 at 21:34
  • $\begingroup$ 3x / (2y) - 7y/(4x) $\endgroup$ – New Zealand's finest Oct 30 '16 at 21:35
  • $\begingroup$ I'm thinking I should be multiplying the 2y and the 7y by 4x, despite it being an expression rather than an equation. $\endgroup$ – New Zealand's finest Oct 30 '16 at 21:37
  • $\begingroup$ I heard good things about New Zealands mathematics, this question kinda amazes me. $\endgroup$ – Anonymous Oct 30 '16 at 21:37
  • $\begingroup$ @NewZealan'sfinest What would the common denominator be here ? $\endgroup$ – Astyx Oct 30 '16 at 21:38

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 $\frac{y}{y}$


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:


  • $\begingroup$ Thanks so much for this explanation, it's super helpful. I wish I could give you five up votes. $\endgroup$ – New Zealand's finest Oct 30 '16 at 21:53
  • 1
    $\begingroup$ I'm glad it's helpful, these questions have given me some difficulty in the pat as well $\endgroup$ – JAP Oct 30 '16 at 21:57

$$\frac{12x^2 - 14y^2 }{8xy}$$

And again, dividing all by $2$,

$$\frac{6x^2 - 7y^2}{4xy}$$

  • 1
    $\begingroup$ your eponym would be so proud. $\endgroup$ – Anonymous Oct 30 '16 at 21:49

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