Solve 1/2x+2-1/4x+4+4/8x^2-8=

$$\frac { 1 } { 2 x + 2 } - \frac { 1 } { 4 x + 4 } + \frac { 4 } { 8 x ^ { 2 } - 8 } =$$

Evaluate

$$\frac{1}{4\left(x-1\right)}$$

Short Solution Steps

Factor 2x+2. Factor 4x+4.

$$\frac{1}{2\left(x+1\right)}-\frac{1}{4\left(x+1\right)}+\frac{4}{8x^{2}-8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+1\right) and 4\left(x+1\right) is 4\left(x+1\right). Multiply \frac{1}{2\left(x+1\right)} times \frac{2}{2}.

$$\frac{2}{4\left(x+1\right)}-\frac{1}{4\left(x+1\right)}+\frac{4}{8x^{2}-8}$$

Since \frac{2}{4\left(x+1\right)} and \frac{1}{4\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators. Subtract 1 from 2 to get 1.

$$\frac{1}{4\left(x+1\right)}+\frac{4}{8x^{2}-8}$$

Factor 8x^{2}-8.

$$\frac{1}{4\left(x+1\right)}+\frac{4}{8\left(x-1\right)\left(x+1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(x+1\right) and 8\left(x-1\right)\left(x+1\right) is 8\left(x-1\right)\left(x+1\right). Multiply \frac{1}{4\left(x+1\right)} times \frac{2\left(x-1\right)}{2\left(x-1\right)}.

$$\frac{2\left(x-1\right)}{8\left(x-1\right)\left(x+1\right)}+\frac{4}{8\left(x-1\right)\left(x+1\right)}$$

Since \frac{2\left(x-1\right)}{8\left(x-1\right)\left(x+1\right)} and \frac{4}{8\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{2\left(x-1\right)+4}{8\left(x-1\right)\left(x+1\right)}$$

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

$$\frac{2x-2+4}{8\left(x-1\right)\left(x+1\right)}$$

Combine like terms in 2x-2+4.

$$\frac{2x+2}{8\left(x-1\right)\left(x+1\right)}$$

Factor the expressions that are not already factored in \frac{2x+2}{8\left(x-1\right)\left(x+1\right)}.

$$\frac{2\left(x+1\right)}{8\left(x-1\right)\left(x+1\right)}$$

Cancel out 2\left(x+1\right) in both numerator and denominator.

$$\frac{1}{4\left(x-1\right)}$$

Expand 4\left(x-1\right).

$$\frac{1}{4x-4}$$

Factor

$$\frac{1}{4\left(x-1\right)}$$