[3p/(12pq + 4q)] รท [8p^2/(6p^2 + 2pq)]
You asked:
Evaluate the expression: \(\frac{\frac{3 p}{12 p q + 4 q}}{\frac{8 \cdot {p}^{2}}{6 \cdot {p}^{2} + 2 p q}}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{\frac{3 p}{12 p q + 4 q}}{\frac{8 \cdot {p}^{2}}{6 \cdot {p}^{2} + 2 p q}} = \frac{3 \cdot \left(6 p^{2} + 2 p q\right)}{8 p \left(12 p q + 4 q\right)} \)
Expanded
\[\frac{\frac{3 p}{12 p q + 4 q}}{\frac{8 \cdot {p}^{2}}{6 \cdot {p}^{2} + 2 p q}} = \frac{9 p}{48 p q + 16 q} + \frac{3 q}{48 p q + 16 q}\]
Factored
\[\frac{\frac{3 p}{12 p q + 4 q}}{\frac{8 \cdot {p}^{2}}{6 \cdot {p}^{2} + 2 p q}} = \frac{3 \cdot \left(3 p + q\right)}{16 q \left(3 p + 1\right)}\]