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

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

Solve for x

$$x = \frac{9}{5} = 1\frac{4}{5} = 1.8$$

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.

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

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

$$x^{2}-4x+3=\left(x+3\right)\left(x-2\right)$$

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

$$x^{2}-4x+3=x^{2}+x-6$$

Subtract x^{2} from both sides.

$$x^{2}-4x+3-x^{2}=x-6$$

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

$$-4x+3=x-6$$

Subtract x from both sides.

$$-4x+3-x=-6$$

Combine -4x and -x to get -5x.

$$-5x+3=-6$$

Subtract 3 from both sides.

$$-5x=-6-3$$

Subtract 3 from -6 to get -9.

$$-5x=-9$$

Divide both sides by -5.

$$x=\frac{-9}{-5}$$

Fraction \frac{-9}{-5} can be simplified to \frac{9}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{9}{5}$$