Solve sqrt{7}(1-1/sqrt{7})+2sqrt{7}-3sqrt{7}

$$\sqrt { 7 } ( 1 - \frac { 1 } { \sqrt { 7 } } ) + 2 \sqrt { 7 } - 3 \sqrt { 7 }$$

Evaluate

$$-1$$

Short Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\sqrt{7}\left(1-\frac{\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\right)+2\sqrt{7}-3\sqrt{7}$$

The square of \sqrt{7} is 7.

$$\sqrt{7}\left(1-\frac{\sqrt{7}}{7}\right)+2\sqrt{7}-3\sqrt{7}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{7}{7}.

$$\sqrt{7}\left(\frac{7}{7}-\frac{\sqrt{7}}{7}\right)+2\sqrt{7}-3\sqrt{7}$$

Since \frac{7}{7} and \frac{\sqrt{7}}{7} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{7}\times \frac{7-\sqrt{7}}{7}+2\sqrt{7}-3\sqrt{7}$$

Express \sqrt{7}\times \frac{7-\sqrt{7}}{7} as a single fraction.

$$\frac{\sqrt{7}\left(7-\sqrt{7}\right)}{7}+2\sqrt{7}-3\sqrt{7}$$

Combine 2\sqrt{7} and -3\sqrt{7} to get -\sqrt{7}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{7} times \frac{7}{7}.

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

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

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

Do the multiplications in \sqrt{7}\left(7-\sqrt{7}\right)-7\sqrt{7}.

$$\frac{7\sqrt{7}-7-7\sqrt{7}}{7}$$

Do the calculations in 7\sqrt{7}-7-7\sqrt{7}.

$$\frac{-7}{7}$$

Divide -7 by 7 to get -1.

$$-1$$

Factor

$$-1$$