Solve (x^2-4y^2)div2y+x/xy*1/x(2y-x)=

$$( x ^ { 2 } - 4 y ^ { 2 } ) \div \frac { 2 y + x } { x y } \cdot \frac { 1 } { x ( 2 y - x ) } =$$

Evaluate

$$-y$$

Short Solution Steps

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

$$\frac{\left(x^{2}-4y^{2}\right)xy}{2y+x}\times \frac{1}{x\left(2y-x\right)}$$

Factor the expressions that are not already factored in \frac{\left(x^{2}-4y^{2}\right)xy}{2y+x}.

$$\frac{xy\left(x-2y\right)\left(x+2y\right)}{x+2y}\times \frac{1}{x\left(2y-x\right)}$$

Cancel out x+2y in both numerator and denominator.

$$xy\left(x-2y\right)\times \frac{1}{x\left(2y-x\right)}$$

Expand the expression.

$$\left(-2xy^{2}+yx^{2}\right)\times \frac{1}{x\left(2y-x\right)}$$

Use the distributive property to multiply x by 2y-x.

$$\left(-2xy^{2}+yx^{2}\right)\times \frac{1}{2xy-x^{2}}$$

Express \left(-2xy^{2}+yx^{2}\right)\times \frac{1}{2xy-x^{2}} as a single fraction.

$$\frac{-2xy^{2}+yx^{2}}{2xy-x^{2}}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in -2y+x.

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

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

$$-y$$

Expand

$$-y$$

Short Solution Steps

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

$$\frac{\left(x^{2}-4y^{2}\right)xy}{2y+x}\times \frac{1}{x\left(2y-x\right)}$$

Factor the expressions that are not already factored in \frac{\left(x^{2}-4y^{2}\right)xy}{2y+x}.

$$\frac{xy\left(x-2y\right)\left(x+2y\right)}{x+2y}\times \frac{1}{x\left(2y-x\right)}$$

Cancel out x+2y in both numerator and denominator.

$$xy\left(x-2y\right)\times \frac{1}{x\left(2y-x\right)}$$

Expand the expression.

$$\left(-2xy^{2}+yx^{2}\right)\times \frac{1}{x\left(2y-x\right)}$$

Use the distributive property to multiply x by 2y-x.

$$\left(-2xy^{2}+yx^{2}\right)\times \frac{1}{2xy-x^{2}}$$

Express \left(-2xy^{2}+yx^{2}\right)\times \frac{1}{2xy-x^{2}} as a single fraction.

$$\frac{-2xy^{2}+yx^{2}}{2xy-x^{2}}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in -2y+x.

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

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

$$-y$$