Solve 2/sqrt{5}-2/sqrt{7}(frac{sqrt{5}}{sqrt{5}}-frac{sqrt{7}}{sqrt{7}}

$$\frac{ 2 }{ \sqrt{ 5 } } - \frac{ 2 }{ \sqrt{ 7 } } ( \frac{ \sqrt{ 5 } }{ \sqrt{ 5 } } - \frac{ \sqrt{ 7 } }{ \sqrt{ 7 } }$$

Evaluate

$$\frac{2\sqrt{5}}{5}\approx 0.894427191$$

Short Solution Steps

Divide \sqrt{5} by \sqrt{5} to get 1.

$$\frac{2}{\sqrt{5}}-\frac{2}{\sqrt{7}}\left(1-\frac{\sqrt{7}}{\sqrt{7}}\right)$$

Divide \sqrt{7} by \sqrt{7} to get 1.

$$\frac{2}{\sqrt{5}}-\frac{2}{\sqrt{7}}\left(1-1\right)$$

Rationalize the denominator of \frac{2}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-\frac{2}{\sqrt{7}}\left(1-1\right)$$

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{5}}{5}-\frac{2}{\sqrt{7}}\left(1-1\right)$$

Rationalize the denominator of \frac{2}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{2\sqrt{5}}{5}-\frac{2\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\left(1-1\right)$$

The square of \sqrt{7} is 7.

$$\frac{2\sqrt{5}}{5}-\frac{2\sqrt{7}}{7}\left(1-1\right)$$

Subtract 1 from 1 to get 0.

$$\frac{2\sqrt{5}}{5}-\frac{2\sqrt{7}}{7}\times 0$$

Anything times zero gives zero.

$$\frac{2\sqrt{5}}{5}-0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 0 times \frac{5}{5}.

$$\frac{2\sqrt{5}}{5}-\frac{0\times 5}{5}$$

Since \frac{2\sqrt{5}}{5} and \frac{0\times 5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\sqrt{5}-0\times 5}{5}$$

Do the multiplications in 2\sqrt{5}-0\times 5.

$$\frac{2\sqrt{5}}{5}$$