Solve 2/x+1+1/(x+1)^2

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 2x+2+1.

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

Expand \left(x+1\right)^{2}.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 2x+2+1.

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

Expand \left(x+1\right)^{2}.

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