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

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

Evaluate

$$\frac{1}{x-2}$$

Short Solution Steps

Factor x^{2}-4.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(x+2\right) and x+2 is \left(x-2\right)\left(x+2\right). Multiply \frac{x+1}{x+2} times \frac{x-2}{x-2}.

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

Since \frac{x^{2}}{\left(x-2\right)\left(x+2\right)} and \frac{\left(x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{2}-\left(x+1\right)\left(x-2\right).

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

Combine like terms in x^{2}-x^{2}+2x-x+2.

$$\frac{x+2}{\left(x-2\right)\left(x+2\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{1}{x-2}$$

Expand

$$\frac{1}{x-2}$$

Short Solution Steps

Factor x^{2}-4.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(x+2\right) and x+2 is \left(x-2\right)\left(x+2\right). Multiply \frac{x+1}{x+2} times \frac{x-2}{x-2}.

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

Since \frac{x^{2}}{\left(x-2\right)\left(x+2\right)} and \frac{\left(x+1\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{2}-\left(x+1\right)\left(x-2\right).

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

Combine like terms in x^{2}-x^{2}+2x-x+2.

$$\frac{x+2}{\left(x-2\right)\left(x+2\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{1}{x-2}$$