Answer
(1) Find the common denominator
(2) Multiply numerator and denominator by missing factor
(3) Then perform the operation.
Work Step by Step
The exercise asks us to use $\frac{3}{x + 5} + \frac{7}{x + 2}$ as an example. Since the denominators have no common factors, the common denominator must then be their multiplication: $(x + 2)(x+5)$. To solve, we multiply numerator and denominator by the missing factor: $$\frac{3}{x + 5} \times (\frac{x+2}{x+2}) + \frac{7}{x + 2} \times (\frac{x+5}{x+5})$$
$= \frac{3(x+2) + 7(x+5)}{(x+2)(x+5)}$; which can be solved easily by using distributive property and factorization for possible simplification.
