Question

simplify. express your answer as a single fraction in simplest form.
\\(\frac{8}{6c + 3} - \frac{c}{12c + 6}\\)

Explanation:

Step1: Factor denominators

Factor \(6c + 3\) as \(3(2c + 1)\), and \(12c + 6\) as \(6(2c + 1)=2\times3(2c + 1)\). So the expression becomes \(\frac{8}{3(2c + 1)}-\frac{c}{6(2c + 1)}\).

Step2: Find common denominator

The least common denominator (LCD) of \(3(2c + 1)\) and \(6(2c + 1)\) is \(6(2c + 1)\). Rewrite the first fraction with LCD: \(\frac{8\times2}{3(2c + 1)\times2}-\frac{c}{6(2c + 1)}=\frac{16}{6(2c + 1)}-\frac{c}{6(2c + 1)}\).

Step3: Subtract the fractions

Subtract the numerators over the common denominator: \(\frac{16 - c}{6(2c + 1)}\).

Answer:

\(\frac{16 - c}{6(2c + 1)}\)