Solve xdiv(2/15+1/6)=(1/9+1/5)div(frac{1}{3}-frac{1}{6})

$$x \div ( \frac{ 2 }{ 15 } + \frac{ 1 }{ 6 } )=( \frac{ 1 }{ 9 } + \frac{ 1 }{ 5 } ) \div ( \frac{ 1 }{ 3 } - \frac{ 1 }{ 6 } )$$

Solve for x

$$x=\frac{14}{25}=0.56$$

Steps for Solving Linear Equation

Least common multiple of 15 and 6 is 30. Convert \frac{2}{15} and \frac{1}{6} to fractions with denominator 30.

$$\frac{x}{\frac{4}{30}+\frac{5}{30}}=\frac{\frac{1}{9}+\frac{1}{5}}{\frac{1}{3}-\frac{1}{6}}$$

Since \frac{4}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{4+5}{30}}=\frac{\frac{1}{9}+\frac{1}{5}}{\frac{1}{3}-\frac{1}{6}}$$

Add 4 and 5 to get 9.

$$\frac{x}{\frac{9}{30}}=\frac{\frac{1}{9}+\frac{1}{5}}{\frac{1}{3}-\frac{1}{6}}$$

Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{1}{9}+\frac{1}{5}}{\frac{1}{3}-\frac{1}{6}}$$

Least common multiple of 9 and 5 is 45. Convert \frac{1}{9} and \frac{1}{5} to fractions with denominator 45.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{5}{45}+\frac{9}{45}}{\frac{1}{3}-\frac{1}{6}}$$

Since \frac{5}{45} and \frac{9}{45} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{5+9}{45}}{\frac{1}{3}-\frac{1}{6}}$$

Add 5 and 9 to get 14.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{14}{45}}{\frac{1}{3}-\frac{1}{6}}$$

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

$$\frac{x}{\frac{3}{10}}=\frac{\frac{14}{45}}{\frac{2}{6}-\frac{1}{6}}$$

Since \frac{2}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{14}{45}}{\frac{2-1}{6}}$$

Subtract 1 from 2 to get 1.

$$\frac{x}{\frac{3}{10}}=\frac{\frac{14}{45}}{\frac{1}{6}}$$

Divide \frac{14}{45} by \frac{1}{6} by multiplying \frac{14}{45} by the reciprocal of \frac{1}{6}.

$$\frac{x}{\frac{3}{10}}=\frac{14}{45}\times 6$$

Express \frac{14}{45}\times 6 as a single fraction.

$$\frac{x}{\frac{3}{10}}=\frac{14\times 6}{45}$$

Multiply 14 and 6 to get 84.

$$\frac{x}{\frac{3}{10}}=\frac{84}{45}$$

Reduce the fraction \frac{84}{45} to lowest terms by extracting and canceling out 3.

$$\frac{x}{\frac{3}{10}}=\frac{28}{15}$$

Multiply both sides by \frac{3}{10}.

$$x=\frac{28}{15}\times \frac{3}{10}$$

Multiply \frac{28}{15} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{28\times 3}{15\times 10}$$

Do the multiplications in the fraction \frac{28\times 3}{15\times 10}.

$$x=\frac{84}{150}$$

Reduce the fraction \frac{84}{150} to lowest terms by extracting and canceling out 6.

$$x=\frac{14}{25}$$