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

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

Evaluate

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

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{2}{x+1} times \frac{x+1}{x+1}.

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

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

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

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

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

Combine like terms in x+2x+2.

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

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

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

Expand

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

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{2}{x+1} times \frac{x+1}{x+1}.

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

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

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

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

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

Combine like terms in x+2x+2.

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

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

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