Checkpoint: Rational Equations: LCD Solution

Solve. Check your solutions for extraneous values.

$n + \frac{n}{n + 4} = \frac{6}{n + 4}$

$\begin{array}{rcl} LCD : (n + 4), n \neq - 4 \\ \frac{n (n + 4)}{n + 4} + \frac{n}{n + 4} & = & \frac{6}{n + 4} \\ n^{2} + 4 n + n & = & 6 \\ n^{2} + 5 n - 6 & = & 0 \\ (n + 6) (n - 1) & = & 0 \\ n & = & - 6, 1 \end{array}$

Note

Q: How do you determine if there are any extraneous solutions?

A: Check the restrictions for the denominator against the values you solved for.

Q: How do you know that the value or values you solved for are correct?

A: Substitute each value, one at a time, into the equation. If both sides of the equation are equal, the answer is correct.