Solve z-8+5/z/z-6+frac{7{z}}

$$\frac { z - 8 + \frac { 5 } { z } } { z - 6 + \frac { 7 } { z } }$$

Evaluate

$$\frac{z^{2}-8z+5}{z^{2}-6z+7}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply z-8 times \frac{z}{z}.

$$\frac{\frac{\left(z-8\right)z}{z}+\frac{5}{z}}{z-6+\frac{7}{z}}$$

Since \frac{\left(z-8\right)z}{z} and \frac{5}{z} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\left(z-8\right)z+5}{z}}{z-6+\frac{7}{z}}$$

Do the multiplications in \left(z-8\right)z+5.

$$\frac{\frac{z^{2}-8z+5}{z}}{z-6+\frac{7}{z}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply z-6 times \frac{z}{z}.

$$\frac{\frac{z^{2}-8z+5}{z}}{\frac{\left(z-6\right)z}{z}+\frac{7}{z}}$$

Since \frac{\left(z-6\right)z}{z} and \frac{7}{z} have the same denominator, add them by adding their numerators.

$$\frac{\frac{z^{2}-8z+5}{z}}{\frac{\left(z-6\right)z+7}{z}}$$

Do the multiplications in \left(z-6\right)z+7.

$$\frac{\frac{z^{2}-8z+5}{z}}{\frac{z^{2}-6z+7}{z}}$$

Divide \frac{z^{2}-8z+5}{z} by \frac{z^{2}-6z+7}{z} by multiplying \frac{z^{2}-8z+5}{z} by the reciprocal of \frac{z^{2}-6z+7}{z}.

$$\frac{\left(z^{2}-8z+5\right)z}{z\left(z^{2}-6z+7\right)}$$

Cancel out z in both numerator and denominator.

$$\frac{z^{2}-8z+5}{z^{2}-6z+7}$$

Expand

$$\frac{z^{2}-8z+5}{z^{2}-6z+7}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply z-8 times \frac{z}{z}.

$$\frac{\frac{\left(z-8\right)z}{z}+\frac{5}{z}}{z-6+\frac{7}{z}}$$

Since \frac{\left(z-8\right)z}{z} and \frac{5}{z} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\left(z-8\right)z+5}{z}}{z-6+\frac{7}{z}}$$

Do the multiplications in \left(z-8\right)z+5.

$$\frac{\frac{z^{2}-8z+5}{z}}{z-6+\frac{7}{z}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply z-6 times \frac{z}{z}.

$$\frac{\frac{z^{2}-8z+5}{z}}{\frac{\left(z-6\right)z}{z}+\frac{7}{z}}$$

Since \frac{\left(z-6\right)z}{z} and \frac{7}{z} have the same denominator, add them by adding their numerators.

$$\frac{\frac{z^{2}-8z+5}{z}}{\frac{\left(z-6\right)z+7}{z}}$$

Do the multiplications in \left(z-6\right)z+7.

$$\frac{\frac{z^{2}-8z+5}{z}}{\frac{z^{2}-6z+7}{z}}$$

Divide \frac{z^{2}-8z+5}{z} by \frac{z^{2}-6z+7}{z} by multiplying \frac{z^{2}-8z+5}{z} by the reciprocal of \frac{z^{2}-6z+7}{z}.

$$\frac{\left(z^{2}-8z+5\right)z}{z\left(z^{2}-6z+7\right)}$$

Cancel out z in both numerator and denominator.

$$\frac{z^{2}-8z+5}{z^{2}-6z+7}$$