Solve 2x+1/x+1+x+3/x

$$\frac { 2 x + 1 } { x + 1 } + \frac { x + 3 } { x }$$

Evaluate

$$\frac{3x^{2}+5x+3}{x\left(x+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+1 and x is x\left(x+1\right). Multiply \frac{2x+1}{x+1} times \frac{x}{x}. Multiply \frac{x+3}{x} times \frac{x+1}{x+1}.

$$\frac{\left(2x+1\right)x}{x\left(x+1\right)}+\frac{\left(x+3\right)\left(x+1\right)}{x\left(x+1\right)}$$

Since \frac{\left(2x+1\right)x}{x\left(x+1\right)} and \frac{\left(x+3\right)\left(x+1\right)}{x\left(x+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(2x+1\right)x+\left(x+3\right)\left(x+1\right)}{x\left(x+1\right)}$$

Do the multiplications in \left(2x+1\right)x+\left(x+3\right)\left(x+1\right).

$$\frac{2x^{2}+x+x^{2}+x+3x+3}{x\left(x+1\right)}$$

Combine like terms in 2x^{2}+x+x^{2}+x+3x+3.

$$\frac{3x^{2}+5x+3}{x\left(x+1\right)}$$

Expand x\left(x+1\right).

$$\frac{3x^{2}+5x+3}{x^{2}+x}$$

Expand

$$\frac{3x^{2}+5x+3}{x\left(x+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+1 and x is x\left(x+1\right). Multiply \frac{2x+1}{x+1} times \frac{x}{x}. Multiply \frac{x+3}{x} times \frac{x+1}{x+1}.

$$\frac{\left(2x+1\right)x}{x\left(x+1\right)}+\frac{\left(x+3\right)\left(x+1\right)}{x\left(x+1\right)}$$

Since \frac{\left(2x+1\right)x}{x\left(x+1\right)} and \frac{\left(x+3\right)\left(x+1\right)}{x\left(x+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(2x+1\right)x+\left(x+3\right)\left(x+1\right)}{x\left(x+1\right)}$$

Do the multiplications in \left(2x+1\right)x+\left(x+3\right)\left(x+1\right).

$$\frac{2x^{2}+x+x^{2}+x+3x+3}{x\left(x+1\right)}$$

Combine like terms in 2x^{2}+x+x^{2}+x+3x+3.

$$\frac{3x^{2}+5x+3}{x\left(x+1\right)}$$

Expand x\left(x+1\right).

$$\frac{3x^{2}+5x+3}{x^{2}+x}$$