Solve x-3/x^2+3x+2+1/-1-x=5/x^2-4

$$\frac{ x-3 }{ { x }^{ 2 } +3x+2 } + \frac{ 1 }{ -1-x } = \frac{ 5 }{ { x }^{ 2 } -4 }$$

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,-1,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+1\right)\left(x+2\right), the least common multiple of x^{2}+3x+2,-1-x,x^{2}-4.

$$\left(x-2\right)\left(x-3\right)+4-x^{2}=\left(x+1\right)\times 5$$

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

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

Add 6 and 4 to get 10.

$$x^{2}-5x+10-x^{2}=\left(x+1\right)\times 5$$

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

$$-5x+10=\left(x+1\right)\times 5$$

Use the distributive property to multiply x+1 by 5.

$$-5x+10=5x+5$$

Subtract 5x from both sides.

$$-5x+10-5x=5$$

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

$$-10x+10=5$$

Subtract 10 from both sides.

$$-10x=5-10$$

Subtract 10 from 5 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.

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