Solve x+1/z^2+zx+x^2*z^3-x^3/zx+z

$$\frac { x + 1 } { z ^ { 2 } + z x + x ^ { 2 } } \cdot \frac { z ^ { 3 } - x ^ { 3 } } { z x + z }$$

Evaluate

$$\frac{z-x}{z}$$

Short Solution Steps

Multiply \frac{x+1}{z^{2}+zx+x^{2}} times \frac{z^{3}-x^{3}}{zx+z} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+1\right)\left(z^{3}-x^{3}\right)}{\left(z^{2}+zx+x^{2}\right)\left(zx+z\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+1\right)\left(-x+z\right)\left(x^{2}+xz+z^{2}\right)}{z\left(x+1\right)\left(x^{2}+xz+z^{2}\right)}$$

Cancel out \left(x+1\right)\left(x^{2}+xz+z^{2}\right) in both numerator and denominator.

$$\frac{-x+z}{z}$$

Expand

$$\frac{z-x}{z}$$

Short Solution Steps

Multiply \frac{x+1}{z^{2}+zx+x^{2}} times \frac{z^{3}-x^{3}}{zx+z} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+1\right)\left(z^{3}-x^{3}\right)}{\left(z^{2}+zx+x^{2}\right)\left(zx+z\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+1\right)\left(-x+z\right)\left(x^{2}+xz+z^{2}\right)}{z\left(x+1\right)\left(x^{2}+xz+z^{2}\right)}$$

Cancel out \left(x+1\right)\left(x^{2}+xz+z^{2}\right) in both numerator and denominator.

$$\frac{-x+z}{z}$$