Solve 2x/x^2+4x+4+1/x+2

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

Evaluate

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

Short Solution Steps

Factor x^{2}+4x+4.

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

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

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

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

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

Combine like terms in 2x+x+2.

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

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

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

Differentiate w.r.t. x

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