Solve x/z+1/x/frac{z{x}+1/x}

$$\frac { \frac { x } { z } + \frac { 1 } { x } } { \frac { z } { x } + \frac { 1 } { x } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of z and x is xz. Multiply \frac{x}{z} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{z}{z}.

$$\frac{\frac{xx}{xz}+\frac{z}{xz}}{\frac{z}{x}+\frac{1}{x}}$$

Since \frac{xx}{xz} and \frac{z}{xz} have the same denominator, add them by adding their numerators.

$$\frac{\frac{xx+z}{xz}}{\frac{z}{x}+\frac{1}{x}}$$

Do the multiplications in xx+z.

$$\frac{\frac{x^{2}+z}{xz}}{\frac{z}{x}+\frac{1}{x}}$$

Since \frac{z}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}+z}{xz}}{\frac{z+1}{x}}$$

Divide \frac{x^{2}+z}{xz} by \frac{z+1}{x} by multiplying \frac{x^{2}+z}{xz} by the reciprocal of \frac{z+1}{x}.

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

Cancel out x in both numerator and denominator.

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

Use the distributive property to multiply z by z+1.

$$\frac{x^{2}+z}{z^{2}+z}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of z and x is xz. Multiply \frac{x}{z} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{z}{z}.

$$\frac{\frac{xx}{xz}+\frac{z}{xz}}{\frac{z}{x}+\frac{1}{x}}$$

Since \frac{xx}{xz} and \frac{z}{xz} have the same denominator, add them by adding their numerators.

$$\frac{\frac{xx+z}{xz}}{\frac{z}{x}+\frac{1}{x}}$$

Do the multiplications in xx+z.

$$\frac{\frac{x^{2}+z}{xz}}{\frac{z}{x}+\frac{1}{x}}$$

Since \frac{z}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}+z}{xz}}{\frac{z+1}{x}}$$

Divide \frac{x^{2}+z}{xz} by \frac{z+1}{x} by multiplying \frac{x^{2}+z}{xz} by the reciprocal of \frac{z+1}{x}.

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

Cancel out x in both numerator and denominator.

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

Use the distributive property to multiply z by z+1.

$$\frac{x^{2}+z}{z^{2}+z}$$