Solve frac{sqrt{11}-1}{4-2/3}+3

$$\frac { \sqrt { 11 } - 1 } { 4 - \frac { 2 } { 3 } } + 3$$

Evaluate

$$\frac{3\left(\sqrt{11}+9\right)}{10}\approx 3.694987437$$

Short Solution Steps

Convert 4 to fraction \frac{12}{3}.

$$\frac{\sqrt{11}-1}{\frac{12}{3}-\frac{2}{3}}+3$$

Since \frac{12}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{11}-1}{\frac{12-2}{3}}+3$$

Subtract 2 from 12 to get 10.

$$\frac{\sqrt{11}-1}{\frac{10}{3}}+3$$

Divide \sqrt{11}-1 by \frac{10}{3} by multiplying \sqrt{11}-1 by the reciprocal of \frac{10}{3}.

$$\frac{\left(\sqrt{11}-1\right)\times 3}{10}+3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{10}{10}.

$$\frac{\left(\sqrt{11}-1\right)\times 3}{10}+\frac{3\times 10}{10}$$

Since \frac{\left(\sqrt{11}-1\right)\times 3}{10} and \frac{3\times 10}{10} have the same denominator, add them by adding their numerators.

$$\frac{\left(\sqrt{11}-1\right)\times 3+3\times 10}{10}$$

Do the multiplications in \left(\sqrt{11}-1\right)\times 3+3\times 10.

$$\frac{3\sqrt{11}-3+30}{10}$$

Do the calculations in 3\sqrt{11}-3+30.

$$\frac{3\sqrt{11}+27}{10}$$

Factor

$$\frac{3 {(\sqrt{11} + 9)}}{10} = 3.69498743710662$$