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

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

Solve for x

$$x=-14$$

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.

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

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

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

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

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

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

$$x^{2}+4x+4=x^{2}+3x-10$$

Subtract x^{2} from both sides.

$$x^{2}+4x+4-x^{2}=3x-10$$

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

$$4x+4=3x-10$$

Subtract 3x from both sides.

$$4x+4-3x=-10$$

Combine 4x and -3x to get x.

$$x+4=-10$$

Subtract 4 from both sides.

$$x=-10-4$$

Subtract 4 from -10 to get -14.

$$x=-14$$