Solve w^3-w^2y/wz-wdiv(w-y/z-1)^2=

$$\frac { w ^ { 3 } - w ^ { 2 } y } { w z - w } \div ( \frac { w - y } { z - 1 } ) ^ { 2 } =$$

Evaluate

$$\frac{w\left(z-1\right)}{w-y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{w^{3}-w^{2}y}{wz-w}.

$$\frac{\frac{\left(-y+w\right)w^{2}}{w\left(z-1\right)}}{\left(\frac{w-y}{z-1}\right)^{2}}$$

Cancel out w in both numerator and denominator.

$$\frac{\frac{w\left(-y+w\right)}{z-1}}{\left(\frac{w-y}{z-1}\right)^{2}}$$

To raise \frac{w-y}{z-1} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{w\left(-y+w\right)}{z-1}}{\frac{\left(w-y\right)^{2}}{\left(z-1\right)^{2}}}$$

Divide \frac{w\left(-y+w\right)}{z-1} by \frac{\left(w-y\right)^{2}}{\left(z-1\right)^{2}} by multiplying \frac{w\left(-y+w\right)}{z-1} by the reciprocal of \frac{\left(w-y\right)^{2}}{\left(z-1\right)^{2}}.

$$\frac{w\left(-y+w\right)\left(z-1\right)^{2}}{\left(z-1\right)\left(w-y\right)^{2}}$$

Cancel out \left(z-1\right)\left(-y+w\right) in both numerator and denominator.

$$\frac{w\left(z-1\right)}{-y+w}$$

Use the distributive property to multiply w by z-1.

$$\frac{wz-w}{-y+w}$$

Expand

$$-\frac{wz-w}{y-w}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{w^{3}-w^{2}y}{wz-w}.

$$\frac{\frac{\left(-y+w\right)w^{2}}{w\left(z-1\right)}}{\left(\frac{w-y}{z-1}\right)^{2}}$$

Cancel out w in both numerator and denominator.

$$\frac{\frac{w\left(-y+w\right)}{z-1}}{\left(\frac{w-y}{z-1}\right)^{2}}$$

To raise \frac{w-y}{z-1} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\frac{w\left(-y+w\right)}{z-1}}{\frac{\left(w-y\right)^{2}}{\left(z-1\right)^{2}}}$$

Divide \frac{w\left(-y+w\right)}{z-1} by \frac{\left(w-y\right)^{2}}{\left(z-1\right)^{2}} by multiplying \frac{w\left(-y+w\right)}{z-1} by the reciprocal of \frac{\left(w-y\right)^{2}}{\left(z-1\right)^{2}}.

$$\frac{w\left(-y+w\right)\left(z-1\right)^{2}}{\left(z-1\right)\left(w-y\right)^{2}}$$

Cancel out \left(z-1\right)\left(-y+w\right) in both numerator and denominator.

$$\frac{w\left(z-1\right)}{-y+w}$$

Use the distributive property to multiply w by z-1.

$$\frac{wz-w}{-y+w}$$