Solve 5/x-1+1/4-2=2

$$\frac { 5 } { x - 1 } + \frac { 1 } { 4 - 2 } = 2$$

Solve for x

$$x = \frac{13}{3} = 4\frac{1}{3} \approx 4.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

$$5+\frac{1}{2}x-\frac{1}{2}=2\left(x-1\right)$$

Subtract \frac{1}{2} from 5 to get \frac{9}{2}.

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

Use the distributive property to multiply 2 by x-1.

$$\frac{9}{2}+\frac{1}{2}x=2x-2$$

Subtract 2x from both sides.

$$\frac{9}{2}+\frac{1}{2}x-2x=-2$$

Combine \frac{1}{2}x and -2x to get -\frac{3}{2}x.

$$\frac{9}{2}-\frac{3}{2}x=-2$$

Subtract \frac{9}{2} from both sides.

$$-\frac{3}{2}x=-2-\frac{9}{2}$$

Subtract \frac{9}{2} from -2 to get -\frac{13}{2}.

$$-\frac{3}{2}x=-\frac{13}{2}$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}.

$$x=-\frac{13}{2}\left(-\frac{2}{3}\right)$$

Multiply -\frac{13}{2} and -\frac{2}{3} to get \frac{13}{3}.

$$x=\frac{13}{3}$$