Solve frac{12/sqrt{13}}{25/sqrt{13}+sqrt{13}}

$$\frac { \frac { 12 } { \sqrt { 13 } } } { \frac { 25 } { \sqrt { 13 } } + \sqrt { 13 } }$$

Evaluate

$$\frac{6}{19}\approx 0.315789474$$

Solution Steps

Rationalize the denominator of \frac{12}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{\frac{12\sqrt{13}}{\left(\sqrt{13}\right)^{2}}}{\frac{25}{\sqrt{13}}+\sqrt{13}}$$

The square of \sqrt{13} is 13.

$$\frac{\frac{12\sqrt{13}}{13}}{\frac{25}{\sqrt{13}}+\sqrt{13}}$$

Rationalize the denominator of \frac{25}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{\frac{12\sqrt{13}}{13}}{\frac{25\sqrt{13}}{\left(\sqrt{13}\right)^{2}}+\sqrt{13}}$$

The square of \sqrt{13} is 13.

$$\frac{\frac{12\sqrt{13}}{13}}{\frac{25\sqrt{13}}{13}+\sqrt{13}}$$

Combine \frac{25\sqrt{13}}{13} and \sqrt{13} to get \frac{38}{13}\sqrt{13}.

$$\frac{\frac{12\sqrt{13}}{13}}{\frac{38}{13}\sqrt{13}}$$

Express \frac{\frac{12\sqrt{13}}{13}}{\frac{38}{13}\sqrt{13}} as a single fraction.

$$\frac{12\sqrt{13}}{13\times \frac{38}{13}\sqrt{13}}$$

Cancel out \sqrt{13} in both numerator and denominator.

$$\frac{12}{\frac{38}{13}\times 13}$$

Cancel out 13 and 13.

$$\frac{12}{38}$$

Reduce the fraction \frac{12}{38} to lowest terms by extracting and canceling out 2.

$$\frac{6}{19}$$

Factor

$$\frac{2 \cdot 3}{19} = 0.3157894736842105$$