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

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

Evaluate

$$\frac{x+6}{4\left(x^{2}-4\right)}$$

Short Solution Steps

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

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

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

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

Combine like terms in 4+x+2.

$$\frac{\frac{6+x}{4\left(x+2\right)}}{x-2}$$

Express \frac{\frac{6+x}{4\left(x+2\right)}}{x-2} as a single fraction.

$$\frac{6+x}{4\left(x+2\right)\left(x-2\right)}$$

Use the distributive property to multiply 4 by x+2.

$$\frac{6+x}{\left(4x+8\right)\left(x-2\right)}$$

Apply the distributive property by multiplying each term of 4x+8 by each term of x-2.

$$\frac{6+x}{4x^{2}-8x+8x-16}$$

Combine -8x and 8x to get 0.

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

Expand

$$\frac{x+6}{4\left(x^{2}-4\right)}$$

Short Solution Steps

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

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

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

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

Combine like terms in 4+x+2.

$$\frac{\frac{6+x}{4\left(x+2\right)}}{x-2}$$

Express \frac{\frac{6+x}{4\left(x+2\right)}}{x-2} as a single fraction.

$$\frac{6+x}{4\left(x+2\right)\left(x-2\right)}$$

Use the distributive property to multiply 4 by x+2.

$$\frac{6+x}{\left(4x+8\right)\left(x-2\right)}$$

Apply the distributive property by multiplying each term of 4x+8 by each term of x-2.

$$\frac{6+x}{4x^{2}-8x+8x-16}$$

Combine -8x and 8x to get 0.

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