Solve frac{z^{3}+t^{3}}{z^{2}-t^2}:z^3-z^2t+zt^2/2z-2t

$$\frac { z ^ { 3 } + t ^ { 3 } } { z ^ { 2 } - t ^ { 2 } } : \frac { z ^ { 3 } - z ^ { 2 } t + z t ^ { 2 } } { 2 z - 2 t }$$

Evaluate

$$\frac{2}{z}$$

Short Solution Steps

Divide \frac{z^{3}+t^{3}}{z^{2}-t^{2}} by \frac{z^{3}-z^{2}t+zt^{2}}{2z-2t} by multiplying \frac{z^{3}+t^{3}}{z^{2}-t^{2}} by the reciprocal of \frac{z^{3}-z^{2}t+zt^{2}}{2z-2t}.

$$\frac{\left(z^{3}+t^{3}\right)\left(2z-2t\right)}{\left(z^{2}-t^{2}\right)\left(z^{3}-z^{2}t+zt^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(z+t\right)\left(z-t\right)\left(z^{2}-tz+t^{2}\right)}{z\left(z+t\right)\left(z-t\right)\left(z^{2}-tz+t^{2}\right)}$$

Cancel out \left(z+t\right)\left(z-t\right)\left(z^{2}-tz+t^{2}\right) in both numerator and denominator.

$$\frac{2}{z}$$

Expand

$$\frac{2}{z}$$

Short Solution Steps

Divide \frac{z^{3}+t^{3}}{z^{2}-t^{2}} by \frac{z^{3}-z^{2}t+zt^{2}}{2z-2t} by multiplying \frac{z^{3}+t^{3}}{z^{2}-t^{2}} by the reciprocal of \frac{z^{3}-z^{2}t+zt^{2}}{2z-2t}.

$$\frac{\left(z^{3}+t^{3}\right)\left(2z-2t\right)}{\left(z^{2}-t^{2}\right)\left(z^{3}-z^{2}t+zt^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(z+t\right)\left(z-t\right)\left(z^{2}-tz+t^{2}\right)}{z\left(z+t\right)\left(z-t\right)\left(z^{2}-tz+t^{2}\right)}$$

Cancel out \left(z+t\right)\left(z-t\right)\left(z^{2}-tz+t^{2}\right) in both numerator and denominator.

$$\frac{2}{z}$$