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

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

Solve for x

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+5\right), the least common multiple of x-1,x+5.

$$\left(x+5\right)\left(x-3\right)=\left(x-1\right)\left(x-6\right)$$

Use the distributive property to multiply x+5 by x-3 and combine like terms.

$$x^{2}+2x-15=\left(x-1\right)\left(x-6\right)$$

Use the distributive property to multiply x-1 by x-6 and combine like terms.

$$x^{2}+2x-15=x^{2}-7x+6$$

Subtract x^{2} from both sides.

$$x^{2}+2x-15-x^{2}=-7x+6$$

Combine x^{2} and -x^{2} to get 0.

$$2x-15=-7x+6$$

Add 7x to both sides.

$$2x-15+7x=6$$

Combine 2x and 7x to get 9x.

$$9x-15=6$$

Add 15 to both sides.

$$9x=6+15$$

Add 6 and 15 to get 21.

$$9x=21$$

Divide both sides by 9.

$$x=\frac{21}{9}$$

Reduce the fraction \frac{21}{9} to lowest terms by extracting and canceling out 3.

$$x=\frac{7}{3}$$