Question

1. simplify the complex rational expression by simplifying the numerator and denominator separately

\\(\frac{1 - \frac{5}{6}}{\frac{1}{24} + 4}\\)
the simplified expression is \\(\square\\). (type an integer or a fraction.)

Explanation:

Step1: Simplify the numerator

First, simplify the numerator \(1 - \frac{5}{6}\). We can write \(1\) as \(\frac{6}{6}\), so \(\frac{6}{6}-\frac{5}{6}=\frac{6 - 5}{6}=\frac{1}{6}\).

Step2: Simplify the denominator

Next, simplify the denominator \(\frac{1}{24}+4\). We can write \(4\) as \(\frac{96}{24}\) (since \(4=\frac{4\times24}{24}=\frac{96}{24}\)), so \(\frac{1}{24}+\frac{96}{24}=\frac{1 + 96}{24}=\frac{97}{24}\).

Step3: Divide the simplified numerator by the simplified denominator

Now we have a complex fraction \(\frac{\frac{1}{6}}{\frac{97}{24}}\). Dividing by a fraction is the same as multiplying by its reciprocal, so \(\frac{1}{6}\div\frac{97}{24}=\frac{1}{6}\times\frac{24}{97}\).
Simplify the multiplication: \(\frac{1\times24}{6\times97}=\frac{24}{582}\). We can simplify this fraction by dividing both the numerator and the denominator by \(6\): \(\frac{24\div6}{582\div6}=\frac{4}{97}\).

Answer:

\(\frac{4}{97}\)