Solve 16-25x^2/3x+ydiv4x-5x^2/9x^2-y^2

$$\frac { 16 - 25 x ^ { 2 } } { 3 x + y } \div \frac { 4 x - 5 x ^ { 2 } } { 9 x ^ { 2 } - y ^ { 2 } }$$

Evaluate

$$\frac{\left(3x-y\right)\left(5x+4\right)}{x}$$

Short Solution Steps

Divide \frac{16-25x^{2}}{3x+y} by \frac{4x-5x^{2}}{9x^{2}-y^{2}} by multiplying \frac{16-25x^{2}}{3x+y} by the reciprocal of \frac{4x-5x^{2}}{9x^{2}-y^{2}}.

$$\frac{\left(16-25x^{2}\right)\left(9x^{2}-y^{2}\right)}{\left(3x+y\right)\left(4x-5x^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(-5x-4\right)\left(5x-4\right)\left(3x+y\right)\left(3x-y\right)}{x\left(-5x+4\right)\left(3x+y\right)}$$

Extract the negative sign in -4+5x.

$$\frac{-\left(-5x-4\right)\left(-5x+4\right)\left(3x+y\right)\left(3x-y\right)}{x\left(-5x+4\right)\left(3x+y\right)}$$

Cancel out \left(-5x+4\right)\left(3x+y\right) in both numerator and denominator.

$$\frac{-\left(-5x-4\right)\left(3x-y\right)}{x}$$

Expand the expression.

$$\frac{15x^{2}-5xy+12x-4y}{x}$$

Expand

$$15x-5y-\frac{4y}{x}+12$$

Short Solution Steps

Divide \frac{16-25x^{2}}{3x+y} by \frac{4x-5x^{2}}{9x^{2}-y^{2}} by multiplying \frac{16-25x^{2}}{3x+y} by the reciprocal of \frac{4x-5x^{2}}{9x^{2}-y^{2}}.

$$\frac{\left(16-25x^{2}\right)\left(9x^{2}-y^{2}\right)}{\left(3x+y\right)\left(4x-5x^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(-5x-4\right)\left(5x-4\right)\left(3x+y\right)\left(3x-y\right)}{x\left(-5x+4\right)\left(3x+y\right)}$$

Extract the negative sign in -4+5x.

$$\frac{-\left(-5x-4\right)\left(-5x+4\right)\left(3x+y\right)\left(3x-y\right)}{x\left(-5x+4\right)\left(3x+y\right)}$$

Cancel out \left(-5x+4\right)\left(3x+y\right) in both numerator and denominator.

$$\frac{-\left(-5x-4\right)\left(3x-y\right)}{x}$$

Expand the expression.

$$\frac{15x^{2}-5xy+12x-4y}{x}$$