Solve x+2/x-4=5

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

Solve for x

$$x = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by x-4.

$$x+2=5\left(x-4\right)$$

Use the distributive property to multiply 5 by x-4.

$$x+2=5x-20$$

Subtract 5x from both sides.

$$x+2-5x=-20$$

Combine x and -5x to get -4x.

$$-4x+2=-20$$

Subtract 2 from both sides.

$$-4x=-20-2$$

Subtract 2 from -20 to get -22.

$$-4x=-22$$

Divide both sides by -4.

$$x=\frac{-22}{-4}$$

Reduce the fraction \frac{-22}{-4} to lowest terms by extracting and canceling out -2.

$$x=\frac{11}{2}$$