Solve x+3/x-2=x+10/x-5

$$\frac { x + 3 } { x - 2 } = \frac { x + 10 } { x - 5 }$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 2,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x-2\right), the least common multiple of x-2,x-5.

$$\left(x-5\right)\left(x+3\right)=\left(x-2\right)\left(x+10\right)$$

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

$$x^{2}-2x-15=\left(x-2\right)\left(x+10\right)$$

Use the distributive property to multiply x-2 by x+10 and combine like terms.

$$x^{2}-2x-15=x^{2}+8x-20$$

Subtract x^{2} from both sides.

$$x^{2}-2x-15-x^{2}=8x-20$$

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

$$-2x-15=8x-20$$

Subtract 8x from both sides.

$$-2x-15-8x=-20$$

Combine -2x and -8x to get -10x.

$$-10x-15=-20$$

Add 15 to both sides.

$$-10x=-20+15$$

Add -20 and 15 to get -5.

$$-10x=-5$$

Divide both sides by -10.

$$x=\frac{-5}{-10}$$

Reduce the fraction \frac{-5}{-10} to lowest terms by extracting and canceling out -5.

$$x=\frac{1}{2}$$