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

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

Solve for x

$$x=\frac{7}{8}=0.875$$

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.

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

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

$$x^{2}-5x+6+4-x^{2}=\left(x+1\right)\times 3$$

Add 6 and 4 to get 10.

$$x^{2}-5x+10-x^{2}=\left(x+1\right)\times 3$$

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

$$-5x+10=\left(x+1\right)\times 3$$

Use the distributive property to multiply x+1 by 3.

$$-5x+10=3x+3$$

Subtract 3x from both sides.

$$-5x+10-3x=3$$

Combine -5x and -3x to get -8x.

$$-8x+10=3$$

Subtract 10 from both sides.

$$-8x=3-10$$

Subtract 10 from 3 to get -7.

$$-8x=-7$$

Divide both sides by -8.

$$x=\frac{-7}{-8}$$

Fraction \frac{-7}{-8} can be simplified to \frac{7}{8} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7}{8}$$