Question

add.
\\(\dfrac{11}{6x - 12} + \dfrac{x}{x - 2}\\)
simplify your answer as much as possible.

Explanation:

Step1: Factor the denominator of the first fraction

Factor \(6x - 12\) to get \(6(x - 2)\). So the expression becomes \(\frac{11}{6(x - 2)}+\frac{x}{x - 2}\).

Step2: Find a common denominator

The common denominator of \(6(x - 2)\) and \(x - 2\) is \(6(x - 2)\). Rewrite the second fraction with the common denominator: \(\frac{x}{x - 2}=\frac{6x}{6(x - 2)}\).

Step3: Add the fractions

Now add the two fractions: \(\frac{11}{6(x - 2)}+\frac{6x}{6(x - 2)}=\frac{11 + 6x}{6(x - 2)}\).

Answer:

\(\frac{6x + 11}{6(x - 2)}\)