Solve 7m/9x-36div8m^2-2m/x^2-16x^2

$$\frac { 7 m } { 9 x - 36 } \div \frac { 8 m ^ { 2 } - 2 m } { x ^ { 2 } - 16 x ^ { 2 } }$$

Evaluate

$$-\frac{35x^{2}}{6\left(x-4\right)\left(4m-1\right)}$$

Short Solution Steps

Divide \frac{7m}{9x-36} by \frac{8m^{2}-2m}{x^{2}-16x^{2}} by multiplying \frac{7m}{9x-36} by the reciprocal of \frac{8m^{2}-2m}{x^{2}-16x^{2}}.

$$\frac{7m\left(x^{2}-16x^{2}\right)}{\left(9x-36\right)\left(8m^{2}-2m\right)}$$

Combine x^{2} and -16x^{2} to get -15x^{2}.

$$\frac{7m\left(-15\right)x^{2}}{\left(9x-36\right)\left(8m^{2}-2m\right)}$$

Multiply 7 and -15 to get -105.

$$\frac{-105mx^{2}}{\left(9x-36\right)\left(8m^{2}-2m\right)}$$

Factor the expressions that are not already factored.

$$\frac{-105mx^{2}}{2\times 9m\left(x-4\right)\left(4m-1\right)}$$

Cancel out 3m in both numerator and denominator.

$$\frac{-35x^{2}}{2\times 3\left(x-4\right)\left(4m-1\right)}$$

Expand the expression.

$$\frac{-35x^{2}}{24mx-6x-96m+24}$$

Expand

$$-\frac{35x^{2}}{6\left(x-4\right)\left(4m-1\right)}$$

Short Solution Steps

Divide \frac{7m}{9x-36} by \frac{8m^{2}-2m}{x^{2}-16x^{2}} by multiplying \frac{7m}{9x-36} by the reciprocal of \frac{8m^{2}-2m}{x^{2}-16x^{2}}.

$$\frac{7m\left(x^{2}-16x^{2}\right)}{\left(9x-36\right)\left(8m^{2}-2m\right)}$$

Combine x^{2} and -16x^{2} to get -15x^{2}.

$$\frac{7m\left(-15\right)x^{2}}{\left(9x-36\right)\left(8m^{2}-2m\right)}$$

Multiply 7 and -15 to get -105.

$$\frac{-105mx^{2}}{\left(9x-36\right)\left(8m^{2}-2m\right)}$$

Factor the expressions that are not already factored.

$$\frac{-105mx^{2}}{2\times 9m\left(x-4\right)\left(4m-1\right)}$$

Cancel out 3m in both numerator and denominator.

$$\frac{-35x^{2}}{2\times 3\left(x-4\right)\left(4m-1\right)}$$

Expand the expression.

$$\frac{-35x^{2}}{24mx-6x-96m+24}$$