Question

simplify the complex rational expression by simplifying the numerator and denomin
\\(\frac{1 - \frac{5}{6}}{\frac{1}{18} + 3}\\)
the simplified expression is \\(\square\\). (type an integer or a fraction )

Explanation:

Step1: Simplify the numerator

The numerator is \(1 - \frac{5}{6}\). We can rewrite \(1\) as \(\frac{6}{6}\), so \(\frac{6}{6}-\frac{5}{6}=\frac{6 - 5}{6}=\frac{1}{6}\).

Step2: Simplify the denominator

The denominator is \(\frac{1}{18}+3\). We rewrite \(3\) as \(\frac{54}{18}\), so \(\frac{1}{18}+\frac{54}{18}=\frac{1 + 54}{18}=\frac{55}{18}\).

Step3: Divide the simplified numerator by the simplified denominator

We have \(\frac{\frac{1}{6}}{\frac{55}{18}}\). Dividing by a fraction is the same as multiplying by its reciprocal, so \(\frac{1}{6}\times\frac{18}{55}\). The \(18\) and \(6\) can be simplified: \(18\div6 = 3\), so we get \(\frac{1\times3}{55}=\frac{3}{55}\).

Answer:

\(\frac{3}{55}\)