Solve m/7text{(1)}2/x^2-4-1/2x-4

$$\frac { m } { 7 } \text { (1) } \frac { 2 } { x ^ { 2 } - 4 } - \frac { 1 } { 2 x - 4 }$$

Evaluate

$$\frac{-7x+4m-14}{14\left(x^{2}-4\right)}$$

$$|x|\neq 2$$

Short Solution Steps

Express \frac{m}{7}\times 1 as a single fraction.

$$\frac{m}{7}\times \frac{2}{x^{2}-4}-\frac{1}{2x-4}$$

Multiply \frac{m}{7} times \frac{2}{x^{2}-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{m\times 2}{7\left(x^{2}-4\right)}-\frac{1}{2x-4}$$

Factor 7\left(x^{2}-4\right). Factor 2x-4.

$$\frac{m\times 2}{7\left(x-2\right)\left(x+2\right)}-\frac{1}{2\left(x-2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7\left(x-2\right)\left(x+2\right) and 2\left(x-2\right) is 14\left(x-2\right)\left(x+2\right). Multiply \frac{m\times 2}{7\left(x-2\right)\left(x+2\right)} times \frac{2}{2}. Multiply \frac{1}{2\left(x-2\right)} times \frac{7\left(x+2\right)}{7\left(x+2\right)}.

$$\frac{2m\times 2}{14\left(x-2\right)\left(x+2\right)}-\frac{7\left(x+2\right)}{14\left(x-2\right)\left(x+2\right)}$$

Since \frac{2m\times 2}{14\left(x-2\right)\left(x+2\right)} and \frac{7\left(x+2\right)}{14\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2m\times 2-7\left(x+2\right)}{14\left(x-2\right)\left(x+2\right)}$$

Do the multiplications in 2m\times 2-7\left(x+2\right).

$$\frac{4m-7x-14}{14\left(x-2\right)\left(x+2\right)}$$

Expand 14\left(x-2\right)\left(x+2\right).

$$\frac{4m-7x-14}{14x^{2}-56}$$

Factor

$$\frac{-7x+4m-14}{14\left(x^{2}-4\right)}$$