Question

Perform the indicated operation.
StartFraction 5 Over x minus 8 EndFraction plus 6
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Part 1

Answer 1

To perform the indicated operation \( \frac{5}{x - 8} + 6 \), you'll first want to express the number 6 in a form that has a common denominator with \( \frac{5}{x - 8} \).

Here’s how you can do that:

1. Rewrite 6 as a fraction with the same denominator:
\[
6 = \frac{6(x - 8)}{x - 8}
\]

2. Now, you can add the two fractions:
\[
\frac{5}{x - 8} + \frac{6(x - 8)}{x - 8} = \frac{5 + 6(x - 8)}{x - 8}
\]

3. Distribute the 6 in the numerator:
\[
= \frac{5 + 6x - 48}{x - 8}
\]

4. Combine like terms in the numerator:
\[
= \frac{6x - 43}{x - 8}
\]

So, the final result of the operation \( \frac{5}{x - 8} + 6 \) is:
\[
\frac{6x - 43}{x - 8}
\]