Solve 36/x^2-4+2+x/2-x=-1

$$\frac { 36 } { x ^ { 2 } - 4 } + \frac { 2 + x } { 2 - x } = - 1$$

Solve for x

$$x=7$$

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}-4,2-x.

$$36-\left(2+x\right)\left(2+x\right)=-\left(x-2\right)\left(x+2\right)$$

Multiply 2+x and 2+x to get \left(2+x\right)^{2}.

$$36-\left(2+x\right)^{2}=-\left(x-2\right)\left(x+2\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2+x\right)^{2}.

$$36-\left(4+4x+x^{2}\right)=-\left(x-2\right)\left(x+2\right)$$

To find the opposite of 4+4x+x^{2}, find the opposite of each term.

$$36-4-4x-x^{2}=-\left(x-2\right)\left(x+2\right)$$

Subtract 4 from 36 to get 32.

$$32-4x-x^{2}=-\left(x-2\right)\left(x+2\right)$$

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

$$32-4x-x^{2}=\left(-x+2\right)\left(x+2\right)$$

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

$$32-4x-x^{2}=-x^{2}+4$$

Add x^{2} to both sides.

$$32-4x-x^{2}+x^{2}=4$$

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

$$32-4x=4$$

Subtract 32 from both sides.

$$-4x=4-32$$

Subtract 32 from 4 to get -28.

$$-4x=-28$$

Divide both sides by -4.

$$x=\frac{-28}{-4}$$

Divide -28 by -4 to get 7.

$$x=7$$