Solve frac{8x^{3}+12x^{2}y}{4x^{2}-9y^{2}}div16x^2y^2/4x^2-12xy+9y^2

$$\frac { 8 x ^ { 3 } + 12 x ^ { 2 } y } { 4 x ^ { 2 } - 9 y ^ { 2 } } \div \frac { 16 x ^ { 2 } y ^ { 2 } } { 4 x ^ { 2 } - 12 x y + 9 y ^ { 2 } }$$

Evaluate

$$\frac{2x-3y}{4y^{2}}$$

Short Solution Steps

Divide \frac{8x^{3}+12x^{2}y}{4x^{2}-9y^{2}} by \frac{16x^{2}y^{2}}{4x^{2}-12xy+9y^{2}} by multiplying \frac{8x^{3}+12x^{2}y}{4x^{2}-9y^{2}} by the reciprocal of \frac{16x^{2}y^{2}}{4x^{2}-12xy+9y^{2}}.

$$\frac{\left(8x^{3}+12x^{2}y\right)\left(4x^{2}-12xy+9y^{2}\right)}{\left(4x^{2}-9y^{2}\right)\times 16x^{2}y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{4\left(2x+3y\right)x^{2}\left(2x-3y\right)^{2}}{16\left(2x-3y\right)\left(2x+3y\right)x^{2}y^{2}}$$

Cancel out 4\left(2x-3y\right)\left(2x+3y\right)x^{2} in both numerator and denominator.

$$\frac{2x-3y}{4y^{2}}$$

Expand

$$-\frac{3y-2x}{4y^{2}}$$

Short Solution Steps

Divide \frac{8x^{3}+12x^{2}y}{4x^{2}-9y^{2}} by \frac{16x^{2}y^{2}}{4x^{2}-12xy+9y^{2}} by multiplying \frac{8x^{3}+12x^{2}y}{4x^{2}-9y^{2}} by the reciprocal of \frac{16x^{2}y^{2}}{4x^{2}-12xy+9y^{2}}.

$$\frac{\left(8x^{3}+12x^{2}y\right)\left(4x^{2}-12xy+9y^{2}\right)}{\left(4x^{2}-9y^{2}\right)\times 16x^{2}y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{4\left(2x+3y\right)x^{2}\left(2x-3y\right)^{2}}{16\left(2x-3y\right)\left(2x+3y\right)x^{2}y^{2}}$$

Cancel out 4\left(2x-3y\right)\left(2x+3y\right)x^{2} in both numerator and denominator.

$$\frac{2x-3y}{4y^{2}}$$