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

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

Solve for x

$$x=2$$

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^{2}+2x-3,x+3,x-1.

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

Use the distributive property to multiply x-1 by 4.

$$x-1+4x-4=x+3$$

Combine x and 4x to get 5x.

$$5x-1-4=x+3$$

Subtract 4 from -1 to get -5.

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

Subtract x from both sides.

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

Combine 5x and -x to get 4x.

$$4x-5=3$$

Add 5 to both sides.

$$4x=3+5$$

Add 3 and 5 to get 8.

$$4x=8$$

Divide both sides by 4.

$$x=\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$x=2$$