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

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

Solve for x

$$x=-\frac{1}{7}\approx -0.142857143$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+3\right), the least common multiple of x+3,x-1.

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

Use the distributive property to multiply x-1 by x-2 and combine like terms.

$$x^{2}-3x+2=\left(x+3\right)\left(x+1\right)$$

Use the distributive property to multiply x+3 by x+1 and combine like terms.

$$x^{2}-3x+2=x^{2}+4x+3$$

Subtract x^{2} from both sides.

$$x^{2}-3x+2-x^{2}=4x+3$$

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

$$-3x+2=4x+3$$

Subtract 4x from both sides.

$$-3x+2-4x=3$$

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

$$-7x+2=3$$

Subtract 2 from both sides.

$$-7x=3-2$$

Subtract 2 from 3 to get 1.

$$-7x=1$$

Divide both sides by -7.

$$x=\frac{1}{-7}$$

Fraction \frac{1}{-7} can be rewritten as -\frac{1}{7} by extracting the negative sign.

$$x=-\frac{1}{7}$$