Solve 2x/2016*2017=1/2016-1/2017

$$\frac { 2 x } { 2016 \times 2017 } = \frac { 1 } { 2016 } - \frac { 1 } { 2017 }$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Cancel out 2 in both numerator and denominator.

$$\frac{x}{1008\times 2017}=\frac{1}{2016}-\frac{1}{2017}$$

Multiply 1008 and 2017 to get 2033136.

$$\frac{x}{2033136}=\frac{1}{2016}-\frac{1}{2017}$$

Least common multiple of 2016 and 2017 is 4066272. Convert \frac{1}{2016} and \frac{1}{2017} to fractions with denominator 4066272.

$$\frac{x}{2033136}=\frac{2017}{4066272}-\frac{2016}{4066272}$$

Since \frac{2017}{4066272} and \frac{2016}{4066272} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{2033136}=\frac{2017-2016}{4066272}$$

Subtract 2016 from 2017 to get 1.

$$\frac{x}{2033136}=\frac{1}{4066272}$$

Multiply both sides by 2033136.

$$x=\frac{1}{4066272}\times 2033136$$

Multiply \frac{1}{4066272} and 2033136 to get \frac{2033136}{4066272}.

$$x=\frac{2033136}{4066272}$$

Reduce the fraction \frac{2033136}{4066272} to lowest terms by extracting and canceling out 2033136.

$$x=\frac{1}{2}$$