Solve 1/x-6-3/x+3=5/x-6

$$\frac { 1 } { x - 6 } - \frac { 3 } { x + 3 } = \frac { 5 } { x - 6 }$$

Solve for x

$$x=\frac{6}{7}\approx 0.857142857$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,6 since division by zero is not defined. Multiply both sides of the equation by \left(x-6\right)\left(x+3\right), the least common multiple of x-6,x+3.

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

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

$$x+3-\left(3x-18\right)=\left(x+3\right)\times 5$$

To find the opposite of 3x-18, find the opposite of each term.

$$x+3-3x+18=\left(x+3\right)\times 5$$

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

$$-2x+3+18=\left(x+3\right)\times 5$$

Add 3 and 18 to get 21.

$$-2x+21=\left(x+3\right)\times 5$$

Use the distributive property to multiply x+3 by 5.

$$-2x+21=5x+15$$

Subtract 5x from both sides.

$$-2x+21-5x=15$$

Combine -2x and -5x to get -7x.

$$-7x+21=15$$

Subtract 21 from both sides.

$$-7x=15-21$$

Subtract 21 from 15 to get -6.

$$-7x=-6$$

Divide both sides by -7.

$$x=\frac{-6}{-7}$$

Fraction \frac{-6}{-7} can be simplified to \frac{6}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{6}{7}$$