Question

simplify. express your answer as a single fraction in simplest form.\\(\frac{8}{4q + 4} - \frac{8}{28q + 28}\\)

Explanation:

Step1: Factor denominators

Factor \(4q + 4\) as \(4(q + 1)\), and \(28q + 28\) as \(28(q + 1)=4\times7(q + 1)\). So the expression becomes \(\frac{8}{4(q + 1)}-\frac{8}{28(q + 1)}\).

Step2: Simplify fractions

Simplify \(\frac{8}{4(q + 1)}\) to \(\frac{2}{q + 1}\), and \(\frac{8}{28(q + 1)}\) to \(\frac{2}{7(q + 1)}\). Now the expression is \(\frac{2}{q + 1}-\frac{2}{7(q + 1)}\).

Step3: Find common denominator

The common denominator of \(q + 1\) and \(7(q + 1)\) is \(7(q + 1)\). Rewrite \(\frac{2}{q + 1}\) as \(\frac{14}{7(q + 1)}\). So we have \(\frac{14}{7(q + 1)}-\frac{2}{7(q + 1)}\).

Step4: Subtract numerators

Subtract the numerators: \(\frac{14 - 2}{7(q + 1)}=\frac{12}{7(q + 1)}\).

Answer:

\(\frac{12}{7(q + 1)}\)