Solve 3h-1/h-7-1/7/h

$$\frac { \frac { 3 h - 1 } { h - 7 } - \frac { 1 } { 7 } } { h }$$

Evaluate

$$\frac{20}{7\left(h-7\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of h-7 and 7 is 7\left(h-7\right). Multiply \frac{3h-1}{h-7} times \frac{7}{7}. Multiply \frac{1}{7} times \frac{h-7}{h-7}.

$$\frac{\frac{7\left(3h-1\right)}{7\left(h-7\right)}-\frac{h-7}{7\left(h-7\right)}}{h}$$

Since \frac{7\left(3h-1\right)}{7\left(h-7\right)} and \frac{h-7}{7\left(h-7\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7\left(3h-1\right)-\left(h-7\right)}{7\left(h-7\right)}}{h}$$

Do the multiplications in 7\left(3h-1\right)-\left(h-7\right).

$$\frac{\frac{21h-7-h+7}{7\left(h-7\right)}}{h}$$

Combine like terms in 21h-7-h+7.

$$\frac{\frac{20h}{7\left(h-7\right)}}{h}$$

Express \frac{\frac{20h}{7\left(h-7\right)}}{h} as a single fraction.

$$\frac{20h}{7\left(h-7\right)h}$$

Cancel out h in both numerator and denominator.

$$\frac{20}{7\left(h-7\right)}$$

Use the distributive property to multiply 7 by h-7.

$$\frac{20}{7h-49}$$

Expand

$$\frac{20}{7\left(h-7\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of h-7 and 7 is 7\left(h-7\right). Multiply \frac{3h-1}{h-7} times \frac{7}{7}. Multiply \frac{1}{7} times \frac{h-7}{h-7}.

$$\frac{\frac{7\left(3h-1\right)}{7\left(h-7\right)}-\frac{h-7}{7\left(h-7\right)}}{h}$$

Since \frac{7\left(3h-1\right)}{7\left(h-7\right)} and \frac{h-7}{7\left(h-7\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7\left(3h-1\right)-\left(h-7\right)}{7\left(h-7\right)}}{h}$$

Do the multiplications in 7\left(3h-1\right)-\left(h-7\right).

$$\frac{\frac{21h-7-h+7}{7\left(h-7\right)}}{h}$$

Combine like terms in 21h-7-h+7.

$$\frac{\frac{20h}{7\left(h-7\right)}}{h}$$

Express \frac{\frac{20h}{7\left(h-7\right)}}{h} as a single fraction.

$$\frac{20h}{7\left(h-7\right)h}$$

Cancel out h in both numerator and denominator.

$$\frac{20}{7\left(h-7\right)}$$

Use the distributive property to multiply 7 by h-7.

$$\frac{20}{7h-49}$$