Solve x-2/x+4=x+1/x-3

$$\frac { x - 2 } { x + 4 } = \frac { x + 1 } { x - 3 }$$

Solve for x

$$x=\frac{1}{5}=0.2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+4\right), the least common multiple of x+4,x-3.

$$\left(x-3\right)\left(x-2\right)=\left(x+4\right)\left(x+1\right)$$

Use the distributive property to multiply x-3 by x-2 and combine like terms.

$$x^{2}-5x+6=\left(x+4\right)\left(x+1\right)$$

Use the distributive property to multiply x+4 by x+1 and combine like terms.

$$x^{2}-5x+6=x^{2}+5x+4$$

Subtract x^{2} from both sides.

$$x^{2}-5x+6-x^{2}=5x+4$$

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

$$-5x+6=5x+4$$

Subtract 5x from both sides.

$$-5x+6-5x=4$$

Combine -5x and -5x to get -10x.

$$-10x+6=4$$

Subtract 6 from both sides.

$$-10x=4-6$$

Subtract 6 from 4 to get -2.

$$-10x=-2$$

Divide both sides by -10.

$$x=\frac{-2}{-10}$$

Reduce the fraction \frac{-2}{-10} to lowest terms by extracting and canceling out -2.

$$x=\frac{1}{5}$$