Solve 2x-3/x-6=5

$$\frac { 2 x - 3 } { x - 6 } = 5$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

Variable x cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by x-6.

$$2x-3=5\left(x-6\right)$$

Use the distributive property to multiply 5 by x-6.

$$2x-3=5x-30$$

Subtract 5x from both sides.

$$2x-3-5x=-30$$

Combine 2x and -5x to get -3x.

$$-3x-3=-30$$

Add 3 to both sides.

$$-3x=-30+3$$

Add -30 and 3 to get -27.

$$-3x=-27$$

Divide both sides by -3.

$$x=\frac{-27}{-3}$$

Divide -27 by -3 to get 9.

$$x=9$$