3p/(12pq+4q) ÷ 〖8p〗^2/(〖6p〗^2+2pq)
You asked:
Evaluate the expression: \(\frac{\frac{\frac{3 p}{12 p q + 4 q}}{{\left( 8 p \right)}^{2}}}{{\left( 6 p \right)}^{2} + 2 p q}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{\frac{\frac{3 p}{12 p q + 4 q}}{{\left( 8 p \right)}^{2}}}{{\left( 6 p \right)}^{2} + 2 p q} = \frac{3}{64 p \left(36 p^{2} + 2 p q\right) \left(12 p q + 4 q\right)} \)
Expanded
\[\frac{\frac{\frac{3 p}{12 p q + 4 q}}{{\left( 8 p \right)}^{2}}}{{\left( 6 p \right)}^{2} + 2 p q} = \frac{3 p}{27648 p^{5} q + 1536 p^{4} q^{2} + 9216 p^{4} q + 512 p^{3} q^{2}}\]
Factored
\[\frac{\frac{\frac{3 p}{12 p q + 4 q}}{{\left( 8 p \right)}^{2}}}{{\left( 6 p \right)}^{2} + 2 p q} = \frac{3}{512 p^{2} q \left(3 p + 1\right) \left(18 p + q\right)}\]