Solve 1/(x+1)^3+3/(x+1)

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

Evaluate

$$\frac{3x^{2}+6x+4}{\left(x+1\right)^{3}}$$

Short Solution Steps

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

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

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

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

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

$$\frac{1+3x^{2}+6x+3}{\left(x+1\right)^{3}}$$

Combine like terms in 1+3x^{2}+6x+3.

$$\frac{4+3x^{2}+6x}{\left(x+1\right)^{3}}$$

Expand \left(x+1\right)^{3}.

$$\frac{4+3x^{2}+6x}{x^{3}+3x^{2}+3x+1}$$

Expand

$$\frac{3x^{2}+6x+4}{\left(x+1\right)^{3}}$$

Short Solution Steps

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

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

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

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

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

$$\frac{1+3x^{2}+6x+3}{\left(x+1\right)^{3}}$$

Combine like terms in 1+3x^{2}+6x+3.

$$\frac{4+3x^{2}+6x}{\left(x+1\right)^{3}}$$

Expand \left(x+1\right)^{3}.

$$\frac{4+3x^{2}+6x}{x^{3}+3x^{2}+3x+1}$$