Problem 30

Question

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{-21}{7 x-14}$$

Step-by-Step Solution

Verified
Answer
The simplified form of the rational expression \(\frac{-21}{7x - 14}\) is \(\frac{-3}{x - 2}\).
1Step 1: Factorize the numerator and denominator
The expression can be rewritten as \(\frac{-3 \times 7}{7 \times (x - 2)}\). The factorization will assist with the identification of common factors.
2Step 2: Cancel out common factors from the numerator and denominator
As we can notice, 7 is a common factor in the numerator and denominator. So, we eliminate it, which leaves us with \(\frac{-3}{x -2}\).
3Step 3: Spot if any more simplification is possible
We verify if there are any more common factors or similar terms to simplify further. As there are no more common factors, this expression is simplified to the fullest.