# Simplify rational expression

How do I simplfy this expression?

$$\dfrac{\frac{x}{2}+\frac{y}{3}}{6x+4y}$$

I tried to use the following rule $\dfrac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\cdot \frac{d}{c}$

But I did not get the right result.

Thanks!!

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I'm not sure what step you took first, but in order to apply that rule, you need to make sure what you're working with has only ONE fraction over ONE fraction. Since the term you have has two fractions in the numerator, you need to combine them first (by finding their GCD and adding). – Petaro Aug 31 '14 at 18:36
Please use another tag. This is not a regular expression. – Frunobulax Aug 31 '14 at 18:37

$$\frac{\frac{x}{2}+\frac{y}{3}}{6x+4y}=\frac{6 \cdot \left ( \frac{x}{2}+\frac{y}{3}\right ) }{6 \cdot (6x+4y)}=\frac{3x+2y}{6 \cdot 2 \cdot (3x+2y)}=\frac{1}{12}$$
It should be added that, for the last passage to be true, the following must hold: $3x+2y \ne 0$. – wil93 Aug 31 '14 at 19:38
$$\frac{\frac{x}{2}+\frac{y}{3}}{6x+4y}$$ Start by simplifying the numerator. Specifically, add the two fractions. $$\frac{\frac{x}{2}+\frac{y}{3}}{6x+4y}=\frac{\frac{3x}{6}+\frac{2y}{6}}{6x+4y}=\frac{\frac{3x+2y}{6}}{6x+4y}$$ Then, since the fraction bar means division, you have: $$\frac{\frac{3x+2y}{6}}{6x+4y}=\frac{3x+2y}{6}\div(6x+4y)$$ And the rest is just the division of two fractions. $$\frac{3x+2y}{6}\div(6x+4y)=\frac{3x+2y}{6}\times\frac{1}{6x+4y}=\frac{3x+2y}{36x+24y}$$ However, we're not done. We need to factor the numerator and denominator and simplify. $$\frac{3x+2y}{36x+24y}=\frac{3x+2y}{12(3x+2y)}=\frac{1}{12}$$