Answer
$\dfrac{8x+23}{(x+1)(x+4)}$
Work Step by Step
Consider the sum of two rational expressions:
$$E=\dfrac{5}{x+1}+\dfrac{3}{x+4}.$$
To add the two rational expressions with different denominators we determine the Least Common Denominator (LCD) of the rational expressions by taking each factor at the highest exponent. In our case the LCD is $(x+1)(x+4)$.
Then we multiply the numerator of each rational expression by the quotient between the LCD and its denominator and place it over the LCD:
$$E=\dfrac{5(x+4)}{(x+1)(x+4)}+\dfrac{3(x+1)}{(x+1)(x+4)}.$$
The next step is to add the numerators of the two rational expressions and place the result over the LCD:
$$E=\dfrac{5x+20+3x+3}{(x+1)(x+4)}=\dfrac{8x+23}{(x+1)(x+4)}.$$
The last step is to simplify the result if possible. In our case it is not possible.
