Solve x+frac{sqrt{2+3}}{sqrt{6/9}}=1

$$x + \frac { \sqrt { 2 + 3 } } { \sqrt { 6 / 9 } } = 1$$

Solve for x

$$x=-\frac{\sqrt{30}}{2}+1\approx -1.738612788$$

Steps for Solving Linear Equation

Add 2 and 3 to get 5.

$$x+\frac{\sqrt{5}}{\sqrt{\frac{6}{9}}}=1$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$x+\frac{\sqrt{5}}{\sqrt{\frac{2}{3}}}=1$$

Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.

$$x+\frac{\sqrt{5}}{\frac{\sqrt{2}}{\sqrt{3}}}=1$$

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

$$x+\frac{\sqrt{5}}{\frac{\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}=1$$

The square of \sqrt{3} is 3.

$$x+\frac{\sqrt{5}}{\frac{\sqrt{2}\sqrt{3}}{3}}=1$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$x+\frac{\sqrt{5}}{\frac{\sqrt{6}}{3}}=1$$

Divide \sqrt{5} by \frac{\sqrt{6}}{3} by multiplying \sqrt{5} by the reciprocal of \frac{\sqrt{6}}{3}.

$$x+\frac{\sqrt{5}\times 3}{\sqrt{6}}=1$$

Rationalize the denominator of \frac{\sqrt{5}\times 3}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$x+\frac{\sqrt{5}\times 3\sqrt{6}}{\left(\sqrt{6}\right)^{2}}=1$$

The square of \sqrt{6} is 6.

$$x+\frac{\sqrt{5}\times 3\sqrt{6}}{6}=1$$

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$x+\frac{\sqrt{30}\times 3}{6}=1$$

Divide \sqrt{30}\times 3 by 6 to get \sqrt{30}\times \frac{1}{2}.

$$x+\sqrt{30}\times \frac{1}{2}=1$$

Subtract \sqrt{30}\times \frac{1}{2} from both sides.

$$x=1-\sqrt{30}\times \frac{1}{2}$$

Multiply -1 and \frac{1}{2} to get -\frac{1}{2}.

$$x=1-\frac{1}{2}\sqrt{30}$$