Question

rational expressions
adding rational expressions with denominators ax and bx: basic
add.
\\(\frac{1}{2c} + \frac{4}{9c}\\)
simplify your answer as much as possible.

Explanation:

Step1: Find the common denominator

The denominators are \(2c\) and \(9c\). The least common denominator (LCD) of \(2c\) and \(9c\) is \(18c\) (since the LCM of 2 and 9 is 18, and we keep the variable \(c\)).

Step2: Rewrite fractions with LCD

Rewrite \(\frac{1}{2c}\) and \(\frac{4}{9c}\) with denominator \(18c\):
\(\frac{1}{2c}=\frac{1\times9}{2c\times9}=\frac{9}{18c}\)
\(\frac{4}{9c}=\frac{4\times2}{9c\times2}=\frac{8}{18c}\)

Step3: Add the fractions

Now add the two fractions: \(\frac{9}{18c}+\frac{8}{18c}=\frac{9 + 8}{18c}=\frac{17}{18c}\)

Answer:

\(\frac{17}{18c}\)