Solve x+3/x+6=x-5/x-8

$$\frac { x + 3 } { x + 6 } = \frac { x - 5 } { x - 8 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -6,8 since division by zero is not defined. Multiply both sides of the equation by \left(x-8\right)\left(x+6\right), the least common multiple of x+6,x-8.

$$\left(x-8\right)\left(x+3\right)=\left(x+6\right)\left(x-5\right)$$

Use the distributive property to multiply x-8 by x+3 and combine like terms.

$$x^{2}-5x-24=\left(x+6\right)\left(x-5\right)$$

Use the distributive property to multiply x+6 by x-5 and combine like terms.

$$x^{2}-5x-24=x^{2}+x-30$$

Subtract x^{2} from both sides.

$$x^{2}-5x-24-x^{2}=x-30$$

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

$$-5x-24=x-30$$

Subtract x from both sides.

$$-5x-24-x=-30$$

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

$$-6x-24=-30$$

Add 24 to both sides.

$$-6x=-30+24$$

Add -30 and 24 to get -6.

$$-6x=-6$$

Divide both sides by -6.

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

Divide -6 by -6 to get 1.

$$x=1$$