Solve frac{p^{2}-36q^{2}}{p^{2}q-14pq^2+49q^3}div18q-3p/p^2-pq-42q^2

$$\frac { p ^ { 2 } - 36 q ^ { 2 } } { p ^ { 2 } q - 14 p q ^ { 2 } + 49 q ^ { 3 } } \div \frac { 18 q - 3 p } { p ^ { 2 } - p q - 42 q ^ { 2 } }$$

Evaluate

$$-\frac{\left(p+6q\right)^{2}}{3q\left(p-7q\right)}$$

Short Solution Steps

Divide \frac{p^{2}-36q^{2}}{p^{2}q-14pq^{2}+49q^{3}} by \frac{18q-3p}{p^{2}-pq-42q^{2}} by multiplying \frac{p^{2}-36q^{2}}{p^{2}q-14pq^{2}+49q^{3}} by the reciprocal of \frac{18q-3p}{p^{2}-pq-42q^{2}}.

$$\frac{\left(p^{2}-36q^{2}\right)\left(p^{2}-pq-42q^{2}\right)}{\left(p^{2}q-14pq^{2}+49q^{3}\right)\left(18q-3p\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(p-7q\right)\left(p-6q\right)\left(p+6q\right)^{2}}{3q\left(-p+6q\right)\left(p-7q\right)^{2}}$$

Extract the negative sign in p-6q.

$$\frac{-\left(p-7q\right)\left(-p+6q\right)\left(p+6q\right)^{2}}{3q\left(-p+6q\right)\left(p-7q\right)^{2}}$$

Cancel out \left(p-7q\right)\left(-p+6q\right) in both numerator and denominator.

$$\frac{-\left(p+6q\right)^{2}}{3q\left(p-7q\right)}$$

Expand the expression.

$$\frac{-p^{2}-12pq-36q^{2}}{3pq-21q^{2}}$$

Expand

$$\frac{p^{2}+12pq+36q^{2}}{3q\left(7q-p\right)}$$

Short Solution Steps

Divide \frac{p^{2}-36q^{2}}{p^{2}q-14pq^{2}+49q^{3}} by \frac{18q-3p}{p^{2}-pq-42q^{2}} by multiplying \frac{p^{2}-36q^{2}}{p^{2}q-14pq^{2}+49q^{3}} by the reciprocal of \frac{18q-3p}{p^{2}-pq-42q^{2}}.

$$\frac{\left(p^{2}-36q^{2}\right)\left(p^{2}-pq-42q^{2}\right)}{\left(p^{2}q-14pq^{2}+49q^{3}\right)\left(18q-3p\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(p-7q\right)\left(p-6q\right)\left(p+6q\right)^{2}}{3q\left(-p+6q\right)\left(p-7q\right)^{2}}$$

Extract the negative sign in p-6q.

$$\frac{-\left(p-7q\right)\left(-p+6q\right)\left(p+6q\right)^{2}}{3q\left(-p+6q\right)\left(p-7q\right)^{2}}$$

Cancel out \left(p-7q\right)\left(-p+6q\right) in both numerator and denominator.

$$\frac{-\left(p+6q\right)^{2}}{3q\left(p-7q\right)}$$

Expand the expression.

$$\frac{-p^{2}-12pq-36q^{2}}{3pq-21q^{2}}$$