Solve sqrt{7/12*7/3}:x=(2/5+1/8):sqrt{(frac{1}{4}-frac{1}{6})*(frac{2}{3}+1)+(3+frac{4}{9})*frac{1}{4}}

$$\sqrt { \frac { 7 } { 12 } \cdot \frac { 7 } { 3 } } : x = ( \frac { 2 } { 5 } + \frac { 1 } { 8 } ) : \sqrt { ( \frac { 1 } { 4 } - \frac { 1 } { 6 } ) \cdot ( \frac { 2 } { 3 } + 1 ) + ( 3 + \frac { 4 } { 9 } ) \cdot \frac { 1 } { 4 } }$$

Solve for x

$$x = \frac{20}{9} = 2\frac{2}{9} \approx 2.222222222$$

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.

$$\sqrt{\frac{7}{12}\times \frac{7}{3}}=x\left(\frac{2}{5}+\frac{1}{8}\right)$$

Multiply \frac{7}{12} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{7\times 7}{12\times 3}}=x\left(\frac{2}{5}+\frac{1}{8}\right)$$

Do the multiplications in the fraction \frac{7\times 7}{12\times 3}.

$$\sqrt{\frac{49}{36}}=x\left(\frac{2}{5}+\frac{1}{8}\right)$$

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.

$$\frac{7}{6}=x\left(\frac{2}{5}+\frac{1}{8}\right)$$

Least common multiple of 5 and 8 is 40. Convert \frac{2}{5} and \frac{1}{8} to fractions with denominator 40.

$$\frac{7}{6}=x\left(\frac{16}{40}+\frac{5}{40}\right)$$

Since \frac{16}{40} and \frac{5}{40} have the same denominator, add them by adding their numerators.

$$\frac{7}{6}=x\times \frac{16+5}{40}$$

Add 16 and 5 to get 21.

$$\frac{7}{6}=x\times \frac{21}{40}$$

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

$$x\times \frac{21}{40}=\frac{7}{6}$$

Multiply both sides by \frac{40}{21}, the reciprocal of \frac{21}{40}.

$$x=\frac{7}{6}\times \frac{40}{21}$$

Multiply \frac{7}{6} times \frac{40}{21} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\times 40}{6\times 21}$$

Do the multiplications in the fraction \frac{7\times 40}{6\times 21}.

$$x=\frac{280}{126}$$

Reduce the fraction \frac{280}{126} to lowest terms by extracting and canceling out 14.

$$x=\frac{20}{9}$$