Solve 5/3-frac{4*frac{4-9sqrt{11}}{5}}{3}

$$\frac{ 5 }{ 3 } - \frac{ 4 \times \frac{ 4-9 \sqrt{ 11 } }{ 5 } }{ 3 }$$

Evaluate

$$\frac{12\sqrt{11}+3}{5}\approx 8.559899497$$

Short Solution Steps

Express 4\times \frac{4-9\sqrt{11}}{5} as a single fraction.

$$\frac{5}{3}-\frac{\frac{4\left(4-9\sqrt{11}\right)}{5}}{3}$$

Express \frac{\frac{4\left(4-9\sqrt{11}\right)}{5}}{3} as a single fraction.

$$\frac{5}{3}-\frac{4\left(4-9\sqrt{11}\right)}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{5}{3}-\frac{4\left(4-9\sqrt{11}\right)}{15}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 15 is 15. Multiply \frac{5}{3} times \frac{5}{5}.

$$\frac{5\times 5}{15}-\frac{4\left(4-9\sqrt{11}\right)}{15}$$

Since \frac{5\times 5}{15} and \frac{4\left(4-9\sqrt{11}\right)}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 5-4\left(4-9\sqrt{11}\right)}{15}$$

Do the multiplications in 5\times 5-4\left(4-9\sqrt{11}\right).

$$\frac{25-16+36\sqrt{11}}{15}$$

Do the calculations in 25-16+36\sqrt{11}.

$$\frac{9+36\sqrt{11}}{15}$$

Factor

$$\frac{3 {(4 \sqrt{11} + 1)}}{5} = 8.55989949685296$$