Problem 64 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

The simplified form of the rational expression \(\frac{x-7}{x+7}\) is the same as the original, as it has no common factors in its numerator and denominator that can be cancelled out.

Step 1: Identify the rational expression

The given rational expression is \(\frac{x-7}{x+7}\)

Step 2: Attempt to simplify

Banking on the principle that we can simplify a rational expression by cancelling out common factors in the numerator and the denominator, we scan the expression for any shared factors. However, in this case, there are no common factors in the numerator \(x-7\) and the denominator \(x+7\) that can be cancelled out.

Step 3: Conclusion

Since we could not find any common factors in the numerator and denominator, we conclude that this rational expression cannot be simplified further. The simplified form of the rational expression is therefore the same as the original, i.e., \(\frac{x-7}{x+7}\)