Solve 2/a+2/b/frac{8{ab}}

$$\frac { \frac { 2 } { a } + \frac { 2 } { b } } { \frac { 8 } { a b } }$$

Evaluate

$$\frac{a+b}{4}$$

Short Solution Steps

Divide \frac{2}{a}+\frac{2}{b} by \frac{8}{ab} by multiplying \frac{2}{a}+\frac{2}{b} by the reciprocal of \frac{8}{ab}.

$$\frac{\left(\frac{2}{a}+\frac{2}{b}\right)ab}{8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and b is ab. Multiply \frac{2}{a} times \frac{b}{b}. Multiply \frac{2}{b} times \frac{a}{a}.

$$\frac{\left(\frac{2b}{ab}+\frac{2a}{ab}\right)ab}{8}$$

Since \frac{2b}{ab} and \frac{2a}{ab} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2b+2a}{ab}ab}{8}$$

Express \frac{2b+2a}{ab}a as a single fraction.

$$\frac{\frac{\left(2b+2a\right)a}{ab}b}{8}$$

Cancel out a in both numerator and denominator.

$$\frac{\frac{2a+2b}{b}b}{8}$$

Cancel out b and b.

$$\frac{2a+2b}{8}$$

Expand

$$\frac{a+b}{4}$$

Short Solution Steps

Divide \frac{2}{a}+\frac{2}{b} by \frac{8}{ab} by multiplying \frac{2}{a}+\frac{2}{b} by the reciprocal of \frac{8}{ab}.

$$\frac{\left(\frac{2}{a}+\frac{2}{b}\right)ab}{8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and b is ab. Multiply \frac{2}{a} times \frac{b}{b}. Multiply \frac{2}{b} times \frac{a}{a}.

$$\frac{\left(\frac{2b}{ab}+\frac{2a}{ab}\right)ab}{8}$$

Since \frac{2b}{ab} and \frac{2a}{ab} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2b+2a}{ab}ab}{8}$$

Express \frac{2b+2a}{ab}a as a single fraction.

$$\frac{\frac{\left(2b+2a\right)a}{ab}b}{8}$$

Cancel out a in both numerator and denominator.

$$\frac{\frac{2a+2b}{b}b}{8}$$

Cancel out b and b.

$$\frac{2a+2b}{8}$$