Question

simplify.
\\(\frac{2b}{3b - 1} + \frac{2b}{b + 3}\\)
a \\(\frac{5b^2 + 13b + 12}{(3b - 1)(b + 3)}
\\)b \\(\frac{8b^2 + 4b}{(3b - 1)(b + 3)}
\\)c \\(\frac{8b^2 + 11b + 6}{(3b - 1)(b + 3)}
\\)d \\(\frac{4b + 2}{4b + 5}\\)

Explanation:

Step1: Find a common denominator

The denominators are \(3b - 1\) and \(b + 3\), so the common denominator is \((3b - 1)(b + 3)\).
Rewrite each fraction with the common denominator:
\(\frac{2b}{3b - 1}=\frac{2b(b + 3)}{(3b - 1)(b + 3)}\)
\(\frac{2b}{b + 3}=\frac{2b(3b - 1)}{(3b - 1)(b + 3)}\)

Step2: Add the numerators

Now add the two fractions:

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Answer:

B. \(\frac{8b^2 + 4b}{(3b - 1)(b + 3)}\)