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

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

Solve for x

$$x=-1$$

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)^{2}, the least common multiple of x^{2}-4x+4,x^{2}-4,x+2.

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

Use the distributive property to multiply x+2 by x-5 and combine like terms.

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

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

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

To find the opposite of 5x-10, find the opposite of each term.

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

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

$$x^{2}-8x-10+10=\left(x-2\right)^{2}$$

Add -10 and 10 to get 0.

$$x^{2}-8x=\left(x-2\right)^{2}$$

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

$$x^{2}-8x=x^{2}-4x+4$$

Subtract x^{2} from both sides.

$$x^{2}-8x-x^{2}=-4x+4$$

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

$$-8x=-4x+4$$

Add 4x to both sides.

$$-8x+4x=4$$

Combine -8x and 4x to get -4x.

$$-4x=4$$

Divide both sides by -4.

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

Divide 4 by -4 to get -1.

$$x=-1$$