Questions: Simplify the rational expression. Select "Cannot be simplified" if applicable. (6 n-12)/(48-24 n)= Cannot be simplified

Solution Steps

To simplify the given rational expression, we need to factor both the numerator and the denominator and then cancel out any common factors.

1. Factor the numerator \(6n - 12\).
2. Factor the denominator \(48 - 24n\).
3. Simplify the expression by canceling out the common factors.

The given rational expression is

\[ \frac{6n - 12}{48 - 24n}. \]

We can factor the numerator \(6n - 12\) as

\[ 6(n - 2). \]

The denominator \(48 - 24n\) can be factored as

\[ 24(2 - n). \]

Substituting the factored forms into the expression, we have:

\[ \frac{6(n - 2)}{24(2 - n)}. \]

Notice that \(2 - n\) can be rewritten as \(-(n - 2)\). Thus, we can express the denominator as:

\[ 24(2 - n) = -24(n - 2). \]

Now, the expression becomes:

\[ \frac{6(n - 2)}{-24(n - 2)}. \]

We can cancel the common factor \((n - 2)\) from the numerator and denominator (assuming \(n \neq 2\)):

\[ \frac{6}{-24} = -\frac{1}{4}. \]

Final Answer