Solve 4x-12/x^2-5x+6-16/x^2-4

$$\frac { 4 x - 12 } { x ^ { 2 } - 5 x + 6 } - \frac { 16 } { x ^ { 2 } - 4 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{4x-12}{x^{2}-5x+6}.

$$\frac{4\left(x-3\right)}{\left(x-3\right)\left(x-2\right)}-\frac{16}{x^{2}-4}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{4}{x-2}-\frac{16}{x^{2}-4}$$

Factor x^{2}-4.

$$\frac{4}{x-2}-\frac{16}{\left(x-2\right)\left(x+2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and \left(x-2\right)\left(x+2\right) is \left(x-2\right)\left(x+2\right). Multiply \frac{4}{x-2} times \frac{x+2}{x+2}.

$$\frac{4\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{16}{\left(x-2\right)\left(x+2\right)}$$

Since \frac{4\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} and \frac{16}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(x+2\right)-16}{\left(x-2\right)\left(x+2\right)}$$

Do the multiplications in 4\left(x+2\right)-16.

$$\frac{4x+8-16}{\left(x-2\right)\left(x+2\right)}$$

Combine like terms in 4x+8-16.

$$\frac{4x-8}{\left(x-2\right)\left(x+2\right)}$$

Factor the expressions that are not already factored in \frac{4x-8}{\left(x-2\right)\left(x+2\right)}.

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

Cancel out x-2 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{4x-12}{x^{2}-5x+6}.

$$\frac{4\left(x-3\right)}{\left(x-3\right)\left(x-2\right)}-\frac{16}{x^{2}-4}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{4}{x-2}-\frac{16}{x^{2}-4}$$

Factor x^{2}-4.

$$\frac{4}{x-2}-\frac{16}{\left(x-2\right)\left(x+2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and \left(x-2\right)\left(x+2\right) is \left(x-2\right)\left(x+2\right). Multiply \frac{4}{x-2} times \frac{x+2}{x+2}.

$$\frac{4\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{16}{\left(x-2\right)\left(x+2\right)}$$

Since \frac{4\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} and \frac{16}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(x+2\right)-16}{\left(x-2\right)\left(x+2\right)}$$

Do the multiplications in 4\left(x+2\right)-16.

$$\frac{4x+8-16}{\left(x-2\right)\left(x+2\right)}$$

Combine like terms in 4x+8-16.

$$\frac{4x-8}{\left(x-2\right)\left(x+2\right)}$$

Factor the expressions that are not already factored in \frac{4x-8}{\left(x-2\right)\left(x+2\right)}.

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

Cancel out x-2 in both numerator and denominator.

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