Solve 4+x/x-2=6

$$\frac { 4 + x } { x - 2 } = 6$$

Solve for x

$$x = \frac{16}{5} = 3\frac{1}{5} = 3.2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.

$$4+x=6\left(x-2\right)$$

Use the distributive property to multiply 6 by x-2.

$$4+x=6x-12$$

Subtract 6x from both sides.

$$4+x-6x=-12$$

Combine x and -6x to get -5x.

$$4-5x=-12$$

Subtract 4 from both sides.

$$-5x=-12-4$$

Subtract 4 from -12 to get -16.

$$-5x=-16$$

Divide both sides by -5.

$$x=\frac{-16}{-5}$$

Fraction \frac{-16}{-5} can be simplified to \frac{16}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{16}{5}$$