Solved: "Perform the indicated operations, and express your answers..."

meplasemamiuk

Answered question

2021-11-16

Perform the indicated operations, and express your answers in simplest form.

\frac{n}{n - 6} + \frac{n + 3}{n + 8} + \frac{12 n + 26}{n^{2} + 2 n - 48}

Answer & Explanation

Clis1955

Beginner2021-11-17Added 9 answers

Step 1
Perform the indicted operation. To add or subtract algebraic fractions having different
Denominators, first find a common denominator, change each fraction to an equivalent fraction with common denominator and then combine each numerator.
Step 2

\frac{n}{n - 6} + \frac{n + 3}{n + 8} + \frac{12 n + 26}{n^{2} + 2 n - 48}

\Rightarrow \frac{n}{n - 6} + \frac{n + 3}{n + 8} + \frac{12 n + 26}{(n - 6) (n + 8)}

\Rightarrow \frac{n (n + 8)}{(n - 6) (n + 8)} + \frac{(n + 3) (n - 6)}{(n + 8) (n - 6)} + \frac{12 n + 26}{(n - 6) (n + 8)} = 0

\Rightarrow \frac{n^{2} + 8 n + n^{2} - 6 n + 3 n - 18 + 12 n + 26}{(n - 6) (n + 8)} = 0

\Rightarrow 2 n^{2} + 17 n + 8 = 0

\Rightarrow 2 n^{2} + 1 n + 16 n + 8 = 0

Step 3

\Rightarrow n (2 n + 1) + 8 (2 n + 1) = 0

\Rightarrow (n + 8) (2 n + 1) = 0

\Rightarrow n = - 8, n = - \frac{1}{2}

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Pre-Algebra

Didn't find what you were looking for?