Solve 4x^2-25y^2/(5y-2x)^2*4/4x+10y

$$\frac { 4 x ^ { 2 } - 25 y ^ { 2 } } { ( 5 y - 2 x ) ^ { 2 } } \times \frac { 4 } { 4 x + 10 y }$$

Evaluate

$$-\frac{2}{5y-2x}$$

Short Solution Steps

Multiply \frac{4x^{2}-25y^{2}}{\left(5y-2x\right)^{2}} times \frac{4}{4x+10y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4x^{2}-25y^{2}\right)\times 4}{\left(5y-2x\right)^{2}\left(4x+10y\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 2\left(2x+5y\right) in both numerator and denominator.

$$\frac{2\left(2x-5y\right)}{\left(-2x+5y\right)^{2}}$$

Expand the expression.

$$\frac{4x-10y}{4x^{2}-20xy+25y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{2\left(2x-5y\right)}{\left(2x-5y\right)^{2}}$$

Cancel out 2x-5y in both numerator and denominator.

$$\frac{2}{2x-5y}$$

Expand

$$-\frac{2}{5\left(-\frac{2x}{5}+y\right)}$$

Short Solution Steps

Multiply \frac{4x^{2}-25y^{2}}{\left(5y-2x\right)^{2}} times \frac{4}{4x+10y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4x^{2}-25y^{2}\right)\times 4}{\left(5y-2x\right)^{2}\left(4x+10y\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 2\left(2x+5y\right) in both numerator and denominator.

$$\frac{2\left(2x-5y\right)}{\left(-2x+5y\right)^{2}}$$

Expand the expression.

$$\frac{4x-10y}{4x^{2}-20xy+25y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{2\left(2x-5y\right)}{\left(2x-5y\right)^{2}}$$

Cancel out 2x-5y in both numerator and denominator.

$$\frac{2}{2x-5y}$$