Solve (3-21/28-3/6)^2:(4/6-1/2)^2=x:frac{1}{36}

$$( 3 - \frac { 21 } { 28 } - \frac { 3 } { 6 } ) ^ { 2 } : ( \frac { 4 } { 6 } - \frac { 1 } { 2 } ) ^ { 2 } = x : \frac { 1 } { 36 }$$

Solve for x

$$x = \frac{49}{16} = 3\frac{1}{16} = 3.0625$$

Steps for Solving Linear Equation

Reduce the fraction \frac{21}{28} to lowest terms by extracting and canceling out 7.

$$\frac{\left(3-\frac{3}{4}-\frac{3}{6}\right)^{2}}{\left(\frac{4}{6}-\frac{1}{2}\right)^{2}}=\frac{x}{\frac{1}{36}}$$

Subtract \frac{3}{4} from 3 to get \frac{9}{4}.

$$\frac{\left(\frac{9}{4}-\frac{3}{6}\right)^{2}}{\left(\frac{4}{6}-\frac{1}{2}\right)^{2}}=\frac{x}{\frac{1}{36}}$$

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

$$\frac{\left(\frac{9}{4}-\frac{1}{2}\right)^{2}}{\left(\frac{4}{6}-\frac{1}{2}\right)^{2}}=\frac{x}{\frac{1}{36}}$$

Subtract \frac{1}{2} from \frac{9}{4} to get \frac{7}{4}.

$$\frac{\left(\frac{7}{4}\right)^{2}}{\left(\frac{4}{6}-\frac{1}{2}\right)^{2}}=\frac{x}{\frac{1}{36}}$$

Calculate \frac{7}{4} to the power of 2 and get \frac{49}{16}.

$$\frac{\frac{49}{16}}{\left(\frac{4}{6}-\frac{1}{2}\right)^{2}}=\frac{x}{\frac{1}{36}}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{49}{16}}{\left(\frac{2}{3}-\frac{1}{2}\right)^{2}}=\frac{x}{\frac{1}{36}}$$

Subtract \frac{1}{2} from \frac{2}{3} to get \frac{1}{6}.

$$\frac{\frac{49}{16}}{\left(\frac{1}{6}\right)^{2}}=\frac{x}{\frac{1}{36}}$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$\frac{\frac{49}{16}}{\frac{1}{36}}=\frac{x}{\frac{1}{36}}$$

Divide \frac{49}{16} by \frac{1}{36} by multiplying \frac{49}{16} by the reciprocal of \frac{1}{36}.

$$\frac{49}{16}\times 36=\frac{x}{\frac{1}{36}}$$

Multiply \frac{49}{16} and 36 to get \frac{441}{4}.

$$\frac{441}{4}=\frac{x}{\frac{1}{36}}$$

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

$$\frac{x}{\frac{1}{36}}=\frac{441}{4}$$

Multiply both sides by \frac{1}{36}.

$$x=\frac{441}{4}\times \frac{1}{36}$$

Multiply \frac{441}{4} and \frac{1}{36} to get \frac{49}{16}.

$$x=\frac{49}{16}$$