Question

add.
\\(\frac{7c + 2}{4c} + \frac{2c - 5}{8c}\\)
simplify your answer as much as possible.

Explanation:

Step1: Find common denominator

The denominators are \(4c\) and \(8c\), the common denominator is \(8c\). Rewrite \(\frac{7c + 2}{4c}\) with denominator \(8c\): multiply numerator and denominator by 2, we get \(\frac{2(7c + 2)}{8c}=\frac{14c + 4}{8c}\)

Step2: Add the fractions

Now add \(\frac{14c + 4}{8c}\) and \(\frac{2c - 5}{8c}\): \(\frac{(14c + 4)+(2c - 5)}{8c}\)

Step3: Simplify the numerator

Combine like terms in the numerator: \(14c+2c + 4-5=16c - 1\)

Step4: Write the final fraction

So the result is \(\frac{16c - 1}{8c}\)

Answer:

\(\frac{16c - 1}{8c}\)