Question

simplify. express your answer as a single fraction in simplest form.
$b + \frac{6b + 2}{b - 5}$

Explanation:

Step1: Convert \( b \) to fraction

To add \( b \) and \( \frac{6b + 2}{b - 5} \), we convert \( b \) to a fraction with denominator \( b - 5 \). So \( b=\frac{b(b - 5)}{b - 5} \).

Step2: Add the two fractions

Now we have \( \frac{b(b - 5)}{b - 5}+\frac{6b + 2}{b - 5} \). Since the denominators are the same, we add the numerators: \( \frac{b(b - 5)+6b + 2}{b - 5} \).

Step3: Expand and simplify numerator

Expand \( b(b - 5) \) to get \( b^{2}-5b \). Then the numerator becomes \( b^{2}-5b + 6b + 2 \). Combine like terms: \( b^{2}+b + 2 \).

Answer:

\( \frac{b^{2}+b + 2}{b - 5} \)