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

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

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+2\right), the least common multiple of x-2,x^{2}-4.

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

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

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

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

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

Use the distributive property to multiply x^{2}-4 by -1.

$$x^{2}+2x-x^{2}+4=1$$

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

$$2x+4=1$$

Subtract 4 from both sides.

$$2x=1-4$$

Subtract 4 from 1 to get -3.

$$2x=-3$$

Divide both sides by 2.

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

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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