Solve 5/x+2+x(x+3)/x^2-4=x/x-2

$$\frac { 5 } { x + 2 } + \frac { x ( x + 3 ) } { x ^ { 2 } - 4 } = \frac { x } { x - 2 }$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

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,x-2.

$$\left(x-2\right)\times 5+x\left(x+3\right)=\left(x+2\right)x$$

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

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

Use the distributive property to multiply x by x+3.

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

Combine 5x and 3x to get 8x.

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

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

$$8x-10+x^{2}=x^{2}+2x$$

Subtract x^{2} from both sides.

$$8x-10+x^{2}-x^{2}=2x$$

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

$$8x-10=2x$$

Subtract 2x from both sides.

$$8x-10-2x=0$$

Combine 8x and -2x to get 6x.

$$6x-10=0$$

Add 10 to both sides. Anything plus zero gives itself.

$$6x=10$$

Divide both sides by 6.

$$x=\frac{10}{6}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{5}{3}$$