Solve 1/x-3-6=-2/x-3

$$\frac { 1 } { x - 3 } - 6 = - \frac { 2 } { x - 3 }$$

Solve for x

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.

$$1+\left(x-3\right)\left(-6\right)=-2$$

Use the distributive property to multiply x-3 by -6.

$$1-6x+18=-2$$

Add 1 and 18 to get 19.

$$19-6x=-2$$

Subtract 19 from both sides.

$$-6x=-2-19$$

Subtract 19 from -2 to get -21.

$$-6x=-21$$

Divide both sides by -6.

$$x=\frac{-21}{-6}$$

Reduce the fraction \frac{-21}{-6} to lowest terms by extracting and canceling out -3.

$$x=\frac{7}{2}$$