Solve 9-16x^2/2x+ydiv3x-4x^2/4x^2-y^2

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

Evaluate

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

Short Solution Steps

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

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -3+4x.

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

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

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

Expand the expression.

$$\frac{8x^{2}-4xy+6x-3y}{x}$$

Expand

$$8x-4y-\frac{3y}{x}+6$$

Short Solution Steps

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

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -3+4x.

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

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

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

Expand the expression.

$$\frac{8x^{2}-4xy+6x-3y}{x}$$