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

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

Evaluate

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

Short Solution Steps

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

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

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

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

Combine like terms in 2+x+1.

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

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

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

Expand

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

Short Solution Steps

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

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

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

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

Combine like terms in 2+x+1.

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

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

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