Simplify rational expression

Question

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!!

Answer 1

$$\frac{\frac{x}{2}+\frac{y}{3}}{6x+4y}=\frac{6 \cdot \left ( \frac{x}{2}+\frac{y}{3}\right ) }{6 \cdot (6x+4y)}=\frac{3x+2y}{6 \cdot 2 \cdot (3x+2y)}=\frac{1}{12}$$

Answer 2

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