Solve frac{sqrt{11x}-x*7/2sqrt{7}}{71}

$$\frac { \sqrt { 11 x } - x \cdot \frac { 7 } { 2 \sqrt { 7 } } } { 71 }$$

Factor

$$\frac{\sqrt{x}\left(-\sqrt{7}\sqrt{x}+2\sqrt{11}\right)}{142}$$

Solution Steps

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

$$factor(\frac{\sqrt{11x}-x\times \frac{7\sqrt{7}}{2\left(\sqrt{7}\right)^{2}}}{71})$$

The square of \sqrt{7} is 7.

$$factor(\frac{\sqrt{11x}-x\times \frac{7\sqrt{7}}{2\times 7}}{71})$$

Cancel out 7 in both numerator and denominator.

$$factor(\frac{\sqrt{11x}-x\times \frac{\sqrt{7}}{2}}{71})$$

Express x\times \frac{\sqrt{7}}{2} as a single fraction.

$$factor(\frac{\sqrt{11x}-\frac{x\sqrt{7}}{2}}{71})$$

Consider \left(11x\right)^{\frac{1}{2}}-\frac{1}{2}x\times 7^{\frac{1}{2}}. Factor out \frac{1}{2}.

$$\frac{2\sqrt{11}\sqrt{x}-x\sqrt{7}}{2}$$

Consider 2\sqrt{11}\sqrt{x}-x\sqrt{7}. Factor out \sqrt{x}.

$$\sqrt{x}\left(2\sqrt{11}-\sqrt{x}\sqrt{7}\right)$$

Rewrite the complete factored expression. Simplify.

$$\frac{\left(2\sqrt{11}-\sqrt{x}\sqrt{7}\right)\sqrt{x}}{142}$$

Evaluate

$$-\frac{\sqrt{7x^{2}}}{142}+\frac{\sqrt{11x}}{71}$$