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

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

Solve for x

$$x = \frac{11}{3} = 3\frac{2}{3} \approx 3.666666667$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+1\right), the least common multiple of x+1,x-2,x^{2}-x-2.

$$\left(x-2\right)\times 5-\left(x+1\right)\times 2=-1$$

Use the distributive property to multiply x-2 by 5.

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

Use the distributive property to multiply x+1 by 2.

$$5x-10-\left(2x+2\right)=-1$$

To find the opposite of 2x+2, find the opposite of each term.

$$5x-10-2x-2=-1$$

Combine 5x and -2x to get 3x.

$$3x-10-2=-1$$

Subtract 2 from -10 to get -12.

$$3x-12=-1$$

Add 12 to both sides.

$$3x=-1+12$$

Add -1 and 12 to get 11.

$$3x=11$$

Divide both sides by 3.

$$x=\frac{11}{3}$$