Solve 1/h+1/k/frac{1{hk}}

$$\frac { \frac { 1 } { h } + \frac { 1 } { k } } { \frac { 1 } { h k } }$$

Evaluate

$$h+k$$

Solution Steps

Divide \frac{1}{h}+\frac{1}{k} by \frac{1}{hk} by multiplying \frac{1}{h}+\frac{1}{k} by the reciprocal of \frac{1}{hk}.

$$\left(\frac{1}{h}+\frac{1}{k}\right)hk$$

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

$$\left(\frac{k}{hk}+\frac{h}{hk}\right)hk$$

Since \frac{k}{hk} and \frac{h}{hk} have the same denominator, add them by adding their numerators.

$$\frac{k+h}{hk}hk$$

Express \frac{k+h}{hk}h as a single fraction.

$$\frac{\left(k+h\right)h}{hk}k$$

Cancel out h in both numerator and denominator.

$$\frac{h+k}{k}k$$

Cancel out k and k.

$$h+k$$

Expand

$$h+k$$

Solution Steps

Divide \frac{1}{h}+\frac{1}{k} by \frac{1}{hk} by multiplying \frac{1}{h}+\frac{1}{k} by the reciprocal of \frac{1}{hk}.

$$\left(\frac{1}{h}+\frac{1}{k}\right)hk$$

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

$$\left(\frac{k}{hk}+\frac{h}{hk}\right)hk$$

Since \frac{k}{hk} and \frac{h}{hk} have the same denominator, add them by adding their numerators.

$$\frac{k+h}{hk}hk$$

Express \frac{k+h}{hk}h as a single fraction.

$$\frac{\left(k+h\right)h}{hk}k$$

Cancel out h in both numerator and denominator.

$$\frac{h+k}{k}k$$

Cancel out k and k.

$$h+k$$