simplify

[3p/(12pq + 4q)] รท [8p^2/(6p^2 + 2pq)]

asked by guest
on Nov 18, 2024 at 9:30 am



You asked:

Simplify the expression: \(\frac{\frac{3 p}{12 p q + 4 q}}{\frac{8 {p}^{2}}{6 {p}^{2} + 2 p q}}\)

MathBot Answer:

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:

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


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