Solve 1/(x^2+3)+1/(x+4)=

$$\frac { 1 } { ( x ^ { 2 } + 3 ) } + \frac { 1 } { ( x + 4 ) } =$$

Evaluate

$$\frac{x^{2}+x+7}{\left(x+4\right)\left(x^{2}+3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2}+3 and x+4 is \left(x+4\right)\left(x^{2}+3\right). Multiply \frac{1}{x^{2}+3} times \frac{x+4}{x+4}. Multiply \frac{1}{x+4} times \frac{x^{2}+3}{x^{2}+3}.

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

Since \frac{x+4}{\left(x+4\right)\left(x^{2}+3\right)} and \frac{x^{2}+3}{\left(x+4\right)\left(x^{2}+3\right)} have the same denominator, add them by adding their numerators.

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

Combine like terms in x+4+x^{2}+3.

$$\frac{x+7+x^{2}}{\left(x+4\right)\left(x^{2}+3\right)}$$

Expand \left(x+4\right)\left(x^{2}+3\right).

$$\frac{x+7+x^{2}}{x^{3}+4x^{2}+3x+12}$$

Differentiate w.r.t. x

$$-\frac{x^{4}+2x^{3}+22x^{2}+32x+9}{\left(\left(x+4\right)\left(x^{2}+3\right)\right)^{2}}$$