Question

Simplify the expression. $$\frac{-3}{x-4} \cdot \frac{x-4}{12(x-7)}$$

Short answer

The simplified expression is \(\frac{-1}{4(x-7)}\).

Step-by-step solution

Identify common factors

In the fractions, observe the factor \(x-4\) that appears in both numerator and denominator. This is a common factor that can simplify the expression.

Cancel the common factors

Cancel the common factor \(x-4\) from the numerator and the denominator. Now the new expression will be \(\frac{-3}{12(x-7)}\).

Simplify the expression further

In the denominator 12 can be simplified as \(3\times4\). Then, one \(3\) in the numerator and another \(3\) in the denominator cancel each other, resulting in \(\frac{-1}{4(x-7)}\).