Solve x+4/x+x/x+4

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

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in \left(x+4\right)\left(x+4\right)+xx.

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

Combine like terms in x^{2}+4x+4x+16+x^{2}.

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

Expand x\left(x+4\right).

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

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in \left(x+4\right)\left(x+4\right)+xx.

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

Combine like terms in x^{2}+4x+4x+16+x^{2}.

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

Expand x\left(x+4\right).

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