Solve frac{{2x^2+3x+1}(2x+1}{x+1}

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

Evaluate

$$\frac{2x^{3}+5x^{2}+5x+1}{x+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{2}+3x times \frac{x+1}{x+1}.

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

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

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

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

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

Combine like terms in 2x^{3}+2x^{2}+3x^{2}+3x+2x+1.

$$\frac{2x^{3}+5x^{2}+5x+1}{x+1}$$

Expand

$$\frac{2x^{3}+5x^{2}+5x+1}{x+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{2}+3x times \frac{x+1}{x+1}.

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

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

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

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

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

Combine like terms in 2x^{3}+2x^{2}+3x^{2}+3x+2x+1.

$$\frac{2x^{3}+5x^{2}+5x+1}{x+1}$$