Solve a^2-4b^2/2ab/frac{1{2b}-1/a}

$$\frac{ \frac{ { a }^{ 2 } -4 { b }^{ 2 } }{ 2ab } }{ \frac{ 1 }{ 2b } - \frac{ 1 }{ a } }$$

Evaluate

$$a+2b$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2b and a is 2ab. Multiply \frac{1}{2b} times \frac{a}{a}. Multiply \frac{1}{a} times \frac{2b}{2b}.

$$\frac{\frac{a^{2}-4b^{2}}{2ab}}{\frac{a}{2ab}-\frac{2b}{2ab}}$$

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

$$\frac{\frac{a^{2}-4b^{2}}{2ab}}{\frac{a-2b}{2ab}}$$

Divide \frac{a^{2}-4b^{2}}{2ab} by \frac{a-2b}{2ab} by multiplying \frac{a^{2}-4b^{2}}{2ab} by the reciprocal of \frac{a-2b}{2ab}.

$$\frac{\left(a^{2}-4b^{2}\right)\times 2ab}{2ab\left(a-2b\right)}$$

Cancel out 2ab in both numerator and denominator.

$$\frac{a^{2}-4b^{2}}{a-2b}$$

Factor the expressions that are not already factored.

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

Cancel out a-2b in both numerator and denominator.

$$a+2b$$

Expand

$$a+2b$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2b and a is 2ab. Multiply \frac{1}{2b} times \frac{a}{a}. Multiply \frac{1}{a} times \frac{2b}{2b}.

$$\frac{\frac{a^{2}-4b^{2}}{2ab}}{\frac{a}{2ab}-\frac{2b}{2ab}}$$

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

$$\frac{\frac{a^{2}-4b^{2}}{2ab}}{\frac{a-2b}{2ab}}$$

Divide \frac{a^{2}-4b^{2}}{2ab} by \frac{a-2b}{2ab} by multiplying \frac{a^{2}-4b^{2}}{2ab} by the reciprocal of \frac{a-2b}{2ab}.

$$\frac{\left(a^{2}-4b^{2}\right)\times 2ab}{2ab\left(a-2b\right)}$$

Cancel out 2ab in both numerator and denominator.

$$\frac{a^{2}-4b^{2}}{a-2b}$$

Factor the expressions that are not already factored.

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

Cancel out a-2b in both numerator and denominator.

$$a+2b$$