Solve 3/x+3+2/x^2+6x+9

$$\frac { 3 } { x + 3 } + \frac { 2 } { x ^ { 2 } + 6 x + 9 }$$

Evaluate

$$\frac{3x+11}{\left(x+3\right)^{2}}$$

Short Solution Steps

Factor x^{2}+6x+9.

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

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

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

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

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

Do the multiplications in 3\left(x+3\right)+2.

$$\frac{3x+9+2}{\left(x+3\right)^{2}}$$

Combine like terms in 3x+9+2.

$$\frac{3x+11}{\left(x+3\right)^{2}}$$

Expand \left(x+3\right)^{2}.

$$\frac{3x+11}{x^{2}+6x+9}$$

Differentiate w.r.t. x

$$\frac{-3x-13}{\left(x+3\right)^{3}}$$