Answer
See explanations.
Work Step by Step
Step 1. Identify x values which need to be excluded from the domain of the two expressions. In the example, $x\ne -5, -2$
Step 2. Find the least common denominator (LCD). In the example, $LCD=(x+5)(x+2)$
Step 3. Convert each expression to have LCD as its denominator. In the example $\frac{x}{x+5}\frac{x+2}{x+2}+\frac{7}{x+2}\frac{x+5}{x+5}=\frac{x^2+5x}{(x+5)(x+2)}+\frac{7x+35}{(x+2)(x+5)}$
Step 4. Since they now have a common denominator, just proceed with the addition or subtraction of the numerators to get the result and simplify as necessary. In the example, we have $\frac{x^2+5x}{(x+5)(x+2)}+\frac{7x+35}{(x+2)(x+5)}=\frac{x^2+12x+35}{(x+2)(x+5)}=\frac{(x+5)(x+7)}{(x+2)(x+5)}=\frac{x+7}{x+2}$
