Math Problem Solver

Simplified:

$$\frac{\frac{3 p}{12 p q + 4 q}}{\frac{8 {p}^{2}}{6 {p}^{2} + 2 p q}} = \frac{3 \cdot \left(3 p + q\right)}{16 q \left(3 p + 1\right)}$$

$$\begin{aligned}\frac{3 p}{\left(12 p q + 4 q\right) \frac{8 p^{2}}{6 p^{2} + 2 p q}}&=\frac{3 p \left(6 p^{2} + 2 p q\right)}{\left(4 q + 12 p q\right) 8 p^{2}}\\&=\frac{3 p \left(3 p + q\right)}{4 p \left(4 q + 12 p q\right)}\\&=\frac{3 q + 9 p}{16 q + 48 p q}\\&=\frac{3 \cdot \left(3 p + q\right)}{16 q \left(3 p + 1\right)}\end{aligned}$$

Expanded:

$$\frac{\frac{3 p}{12 p q + 4 q}}{\frac{8 {p}^{2}}{6 {p}^{2} + 2 p q}} = \frac{9 p}{48 p q + 16 q} + \frac{3 q}{48 p q + 16 q}$$

Factored:

$$\frac{\frac{3 p}{12 p q + 4 q}}{\frac{8 {p}^{2}}{6 {p}^{2} + 2 p q}} = \frac{3 \cdot \left(3 p + q\right)}{16 q \left(3 p + 1\right)}$$