Solve x+4/x-2=x-5/x-8

$$\frac { x + 4 } { x - 2 } = \frac { x - 5 } { x - 8 }$$

Solve for x

$$x=14$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 2,8 since division by zero is not defined. Multiply both sides of the equation by \left(x-8\right)\left(x-2\right), the least common multiple of x-2,x-8.

$$\left(x-8\right)\left(x+4\right)=\left(x-2\right)\left(x-5\right)$$

Use the distributive property to multiply x-8 by x+4 and combine like terms.

$$x^{2}-4x-32=\left(x-2\right)\left(x-5\right)$$

Use the distributive property to multiply x-2 by x-5 and combine like terms.

$$x^{2}-4x-32=x^{2}-7x+10$$

Subtract x^{2} from both sides.

$$x^{2}-4x-32-x^{2}=-7x+10$$

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

$$-4x-32=-7x+10$$

Add 7x to both sides.

$$-4x-32+7x=10$$

Combine -4x and 7x to get 3x.

$$3x-32=10$$

Add 32 to both sides.

$$3x=10+32$$

Add 10 and 32 to get 42.

$$3x=42$$

Divide both sides by 3.

$$x=\frac{42}{3}$$

Divide 42 by 3 to get 14.

$$x=14$$