Solve 1/5+9/z/frac{1{7}-8/z}

$$\frac { \frac { 1 } { 5 } + \frac { 9 } { z } } { \frac { 1 } { 7 } - \frac { 8 } { z } }$$

Evaluate

$$\frac{7\left(z+45\right)}{5\left(z-56\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and z is 5z. Multiply \frac{1}{5} times \frac{z}{z}. Multiply \frac{9}{z} times \frac{5}{5}.

$$\frac{\frac{z}{5z}+\frac{9\times 5}{5z}}{\frac{1}{7}-\frac{8}{z}}$$

Since \frac{z}{5z} and \frac{9\times 5}{5z} have the same denominator, add them by adding their numerators.

$$\frac{\frac{z+9\times 5}{5z}}{\frac{1}{7}-\frac{8}{z}}$$

Do the multiplications in z+9\times 5.

$$\frac{\frac{z+45}{5z}}{\frac{1}{7}-\frac{8}{z}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and z is 7z. Multiply \frac{1}{7} times \frac{z}{z}. Multiply \frac{8}{z} times \frac{7}{7}.

$$\frac{\frac{z+45}{5z}}{\frac{z}{7z}-\frac{8\times 7}{7z}}$$

Since \frac{z}{7z} and \frac{8\times 7}{7z} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{z+45}{5z}}{\frac{z-8\times 7}{7z}}$$

Do the multiplications in z-8\times 7.

$$\frac{\frac{z+45}{5z}}{\frac{z-56}{7z}}$$

Divide \frac{z+45}{5z} by \frac{z-56}{7z} by multiplying \frac{z+45}{5z} by the reciprocal of \frac{z-56}{7z}.

$$\frac{\left(z+45\right)\times 7z}{5z\left(z-56\right)}$$

Cancel out z in both numerator and denominator.

$$\frac{7\left(z+45\right)}{5\left(z-56\right)}$$

Use the distributive property to multiply 7 by z+45.

$$\frac{7z+315}{5\left(z-56\right)}$$

Use the distributive property to multiply 5 by z-56.

$$\frac{7z+315}{5z-280}$$

Expand

$$\frac{7\left(z+45\right)}{5\left(z-56\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and z is 5z. Multiply \frac{1}{5} times \frac{z}{z}. Multiply \frac{9}{z} times \frac{5}{5}.

$$\frac{\frac{z}{5z}+\frac{9\times 5}{5z}}{\frac{1}{7}-\frac{8}{z}}$$

Since \frac{z}{5z} and \frac{9\times 5}{5z} have the same denominator, add them by adding their numerators.

$$\frac{\frac{z+9\times 5}{5z}}{\frac{1}{7}-\frac{8}{z}}$$

Do the multiplications in z+9\times 5.

$$\frac{\frac{z+45}{5z}}{\frac{1}{7}-\frac{8}{z}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and z is 7z. Multiply \frac{1}{7} times \frac{z}{z}. Multiply \frac{8}{z} times \frac{7}{7}.

$$\frac{\frac{z+45}{5z}}{\frac{z}{7z}-\frac{8\times 7}{7z}}$$

Since \frac{z}{7z} and \frac{8\times 7}{7z} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{z+45}{5z}}{\frac{z-8\times 7}{7z}}$$

Do the multiplications in z-8\times 7.

$$\frac{\frac{z+45}{5z}}{\frac{z-56}{7z}}$$

Divide \frac{z+45}{5z} by \frac{z-56}{7z} by multiplying \frac{z+45}{5z} by the reciprocal of \frac{z-56}{7z}.

$$\frac{\left(z+45\right)\times 7z}{5z\left(z-56\right)}$$

Cancel out z in both numerator and denominator.

$$\frac{7\left(z+45\right)}{5\left(z-56\right)}$$

Use the distributive property to multiply 7 by z+45.

$$\frac{7z+315}{5\left(z-56\right)}$$

Use the distributive property to multiply 5 by z-56.

$$\frac{7z+315}{5z-280}$$