Solve sqrt{4/3+1/9-1/12}:x=(1/3+frac{1}{2}):sqrt{(frac{1}{9}+frac{4}{3}*frac{3}{5}-frac{4}{15}):frac{29}{5}}

$$\sqrt { \frac { 4 } { 3 } + \frac { 1 } { 9 } - \frac { 1 } { 12 } } : x = ( \frac { 1 } { 3 } + \frac { 1 } { 2 } ) : \sqrt { ( \frac { 1 } { 9 } + \frac { 4 } { 3 } \cdot \frac { 3 } { 5 } - \frac { 4 } { 15 } ) : \frac { 29 } { 5 } }$$

Solve for x

$$x=\frac{7}{15}\approx 0.466666667$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\sqrt{\frac{4}{3}+\frac{1}{9}-\frac{1}{12}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Least common multiple of 3 and 9 is 9. Convert \frac{4}{3} and \frac{1}{9} to fractions with denominator 9.

$$\sqrt{\frac{12}{9}+\frac{1}{9}-\frac{1}{12}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Since \frac{12}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{12+1}{9}-\frac{1}{12}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Add 12 and 1 to get 13.

$$\sqrt{\frac{13}{9}-\frac{1}{12}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Least common multiple of 9 and 12 is 36. Convert \frac{13}{9} and \frac{1}{12} to fractions with denominator 36.

$$\sqrt{\frac{52}{36}-\frac{3}{36}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Since \frac{52}{36} and \frac{3}{36} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{52-3}{36}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Subtract 3 from 52 to get 49.

$$\sqrt{\frac{49}{36}}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Rewrite the square root of the division \frac{49}{36} as the division of square roots \frac{\sqrt{49}}{\sqrt{36}}. Take the square root of both numerator and denominator.

$$\frac{7}{6}=3x\left(\frac{1}{3}+\frac{1}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{7}{6}=3x\left(\frac{2}{6}+\frac{3}{6}\right)$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{7}{6}=3x\times \frac{2+3}{6}$$

Add 2 and 3 to get 5.

$$\frac{7}{6}=3x\times \frac{5}{6}$$

Express 3\times \frac{5}{6} as a single fraction.

$$\frac{7}{6}=\frac{3\times 5}{6}x$$

Multiply 3 and 5 to get 15.

$$\frac{7}{6}=\frac{15}{6}x$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{7}{6}=\frac{5}{2}x$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{5}{2}x=\frac{7}{6}$$

Multiply both sides by \frac{2}{5}, the reciprocal of \frac{5}{2}.

$$x=\frac{7}{6}\times \frac{2}{5}$$

Multiply \frac{7}{6} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\times 2}{6\times 5}$$

Do the multiplications in the fraction \frac{7\times 2}{6\times 5}.

$$x=\frac{14}{30}$$

Reduce the fraction \frac{14}{30} to lowest terms by extracting and canceling out 2.

$$x=\frac{7}{15}$$