Solve 2/5sqrt{46}+4/3-1/5=

$$\frac{ 2 }{ 5 \sqrt{ 46 } } + \frac{ 4 }{ 3 } - \frac{ 1 }{ 5 } =$$

Evaluate

$$\frac{\sqrt{46}}{115}+\frac{17}{15}\approx 1.192310116$$

Short Solution Steps

Rationalize the denominator of \frac{2}{5\sqrt{46}} by multiplying numerator and denominator by \sqrt{46}.

$$\frac{2\sqrt{46}}{5\left(\sqrt{46}\right)^{2}}+\frac{4}{3}-\frac{1}{5}$$

The square of \sqrt{46} is 46.

$$\frac{2\sqrt{46}}{5\times 46}+\frac{4}{3}-\frac{1}{5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{46}}{5\times 23}+\frac{4}{3}-\frac{1}{5}$$

Multiply 5 and 23 to get 115.

$$\frac{\sqrt{46}}{115}+\frac{4}{3}-\frac{1}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{4}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{\sqrt{46}}{115}+\frac{20}{15}-\frac{3}{15}$$

Since \frac{20}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{46}}{115}+\frac{20-3}{15}$$

Subtract 3 from 20 to get 17.

$$\frac{\sqrt{46}}{115}+\frac{17}{15}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 115 and 15 is 345. Multiply \frac{\sqrt{46}}{115} times \frac{3}{3}. Multiply \frac{17}{15} times \frac{23}{23}.

$$\frac{3\sqrt{46}}{345}+\frac{17\times 23}{345}$$

Since \frac{3\sqrt{46}}{345} and \frac{17\times 23}{345} have the same denominator, add them by adding their numerators.

$$\frac{3\sqrt{46}+17\times 23}{345}$$

Do the multiplications in 3\sqrt{46}+17\times 23.

$$\frac{3\sqrt{46}+391}{345}$$

Factor

$$\frac{3 \sqrt{46} + 391}{345} = 1.1923101157952922$$