Solve x^2+3/x^2-4-4x-1/x^2-4

$$\frac { x ^ { 2 } + 3 } { x ^ { 2 } - 4 } - \frac { 4 x - 1 } { x ^ { 2 } - 4 }$$

Evaluate

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

Short Solution Steps

Since \frac{x^{2}+3}{x^{2}-4} and \frac{4x-1}{x^{2}-4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}+3-\left(4x-1\right)}{x^{2}-4}$$

Do the multiplications in x^{2}+3-\left(4x-1\right).

$$\frac{x^{2}+3-4x+1}{x^{2}-4}$$

Combine like terms in x^{2}+3-4x+1.

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

Factor the expressions that are not already factored in \frac{x^{2}+4-4x}{x^{2}-4}.

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

Cancel out x-2 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Since \frac{x^{2}+3}{x^{2}-4} and \frac{4x-1}{x^{2}-4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}+3-\left(4x-1\right)}{x^{2}-4}$$

Do the multiplications in x^{2}+3-\left(4x-1\right).

$$\frac{x^{2}+3-4x+1}{x^{2}-4}$$

Combine like terms in x^{2}+3-4x+1.

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

Factor the expressions that are not already factored in \frac{x^{2}+4-4x}{x^{2}-4}.

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

Cancel out x-2 in both numerator and denominator.

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