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!!

$$\frac{\frac{x}{2}+\frac{y}{3}}{6x+4y}$$
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.
$$\frac{3x+2y}{36x+24y}=\frac{3x+2y}{12(3x+2y)}=\frac{1}{12}$$
