Question

express the sum in the simplest form.
\\(\frac{3x}{x + 5} + \frac{7}{x + 5}\\)
a. \\(\frac{10x}{x + 5}\\)
b. \\(\frac{10x}{x^2 + 10}\\)
c. \\(\frac{3x + 7}{x + 5}\\)
d. \\(\frac{3x + 7}{x^2 + 10}\\)

Explanation:

Step1: Recall rule for adding fractions

When adding fractions with the same denominator, we use the rule $\frac{a}{c}+\frac{b}{c}=\frac{a + b}{c}$, where $c
eq0$. Here, the denominator for both fractions is $x + 5$.

Step2: Apply the rule to the given fractions

For $\frac{3x}{x + 5}+\frac{7}{x + 5}$, since the denominators are the same ($x+5$), we add the numerators: $3x+7$, and keep the same denominator $x + 5$. So the sum is $\frac{3x + 7}{x + 5}$.

Answer:

C. $\frac{3x + 7}{x + 5}$