Solve g*frac{7sqrt{2}}{5sqrt{7}}-frac{2sqrt{7}}{3sqrt{2}}=

$$g \cdot \frac { 7 \sqrt { 2 } } { 5 \sqrt { 7 } } - \frac { 2 \sqrt { 7 } } { 3 \sqrt { 2 } } =$$

Evaluate

$$\frac{\sqrt{14}\left(3g-5\right)}{15}$$

Solution Steps

Rationalize the denominator of \frac{7\sqrt{2}}{5\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$g\times \frac{7\sqrt{2}\sqrt{7}}{5\left(\sqrt{7}\right)^{2}}-\frac{2\sqrt{7}}{3\sqrt{2}}$$

The square of \sqrt{7} is 7.

$$g\times \frac{7\sqrt{2}\sqrt{7}}{5\times 7}-\frac{2\sqrt{7}}{3\sqrt{2}}$$

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

$$g\times \frac{7\sqrt{14}}{5\times 7}-\frac{2\sqrt{7}}{3\sqrt{2}}$$

Multiply 5 and 7 to get 35.

$$g\times \frac{7\sqrt{14}}{35}-\frac{2\sqrt{7}}{3\sqrt{2}}$$

Divide 7\sqrt{14} by 35 to get \frac{1}{5}\sqrt{14}.

$$g\times \frac{1}{5}\sqrt{14}-\frac{2\sqrt{7}}{3\sqrt{2}}$$

Rationalize the denominator of \frac{2\sqrt{7}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$g\times \frac{1}{5}\sqrt{14}-\frac{2\sqrt{7}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$g\times \frac{1}{5}\sqrt{14}-\frac{2\sqrt{7}\sqrt{2}}{3\times 2}$$

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$g\times \frac{1}{5}\sqrt{14}-\frac{2\sqrt{14}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$g\times \frac{1}{5}\sqrt{14}-\frac{2\sqrt{14}}{6}$$

Divide 2\sqrt{14} by 6 to get \frac{1}{3}\sqrt{14}.

$$g\times \frac{1}{5}\sqrt{14}-\frac{1}{3}\sqrt{14}$$

Factor

$$\frac{\sqrt{14}\left(3g-5\right)}{15}$$

Solution Steps

Rationalize the denominator of \frac{7\sqrt{2}}{5\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$factor(g\times \frac{7\sqrt{2}\sqrt{7}}{5\left(\sqrt{7}\right)^{2}}-\frac{2\sqrt{7}}{3\sqrt{2}})$$

The square of \sqrt{7} is 7.

$$factor(g\times \frac{7\sqrt{2}\sqrt{7}}{5\times 7}-\frac{2\sqrt{7}}{3\sqrt{2}})$$

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

$$factor(g\times \frac{7\sqrt{14}}{5\times 7}-\frac{2\sqrt{7}}{3\sqrt{2}})$$

Multiply 5 and 7 to get 35.

$$factor(g\times \frac{7\sqrt{14}}{35}-\frac{2\sqrt{7}}{3\sqrt{2}})$$

Divide 7\sqrt{14} by 35 to get \frac{1}{5}\sqrt{14}.

$$factor(g\times \frac{1}{5}\sqrt{14}-\frac{2\sqrt{7}}{3\sqrt{2}})$$

Rationalize the denominator of \frac{2\sqrt{7}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$factor(g\times \frac{1}{5}\sqrt{14}-\frac{2\sqrt{7}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}})$$

The square of \sqrt{2} is 2.

$$factor(g\times \frac{1}{5}\sqrt{14}-\frac{2\sqrt{7}\sqrt{2}}{3\times 2})$$

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$factor(g\times \frac{1}{5}\sqrt{14}-\frac{2\sqrt{14}}{3\times 2})$$

Multiply 3 and 2 to get 6.

$$factor(g\times \frac{1}{5}\sqrt{14}-\frac{2\sqrt{14}}{6})$$

Divide 2\sqrt{14} by 6 to get \frac{1}{3}\sqrt{14}.

$$factor(g\times \frac{1}{5}\sqrt{14}-\frac{1}{3}\sqrt{14})$$

Factor out \frac{1}{15}.

$$\frac{3g\sqrt{14}-5\sqrt{14}}{15}$$

Consider 3g\sqrt{14}-5\sqrt{14}. Factor out \sqrt{14}.

$$\sqrt{14}\left(3g-5\right)$$

Rewrite the complete factored expression.

$$\frac{\sqrt{14}\left(3g-5\right)}{15}$$