Question

The algorithm for dividing rational expressions applies to only nonzero rational expressions. Why do you think that "nonzero" is specified in the algorithm? What would happen if you applied the algorithm to a rational expression that could be 0 ?

Answer 1

Answer:

• To avoid the improper cancellation of factors that are zero, since 0/0 is undefined.

Explanation:

Such as when you divide fractions, you can divide rational expressions by factoring and simplifying the common factors on the numerator and denominator of the rational expression.

Nevertheless, that might drive you to cancel some factors that, if were not factored, yield the denominator a zero value.

Cancelling factors whose value is zero is wrong, because that means that you are doing an improper operation (dividing zero by zero).

The first step in the algortihm for dividing ratinal expressions is to factor the terms.

Suppose that your rational expression, after being factored has the form:

$\frac{(x-a)(x-b)}{(x-c)(x-a)}$

Where a, b, and c are different constants.

The next step in the algorithm would be cancel the common factors, which would lead to:

• $\frac{x-a}{x-c}$

Meaning that you cancel (x - a) / (x - a).

• If x - a is equal to zero, that would mean that you cancelled 0 / 0.

You cannot cancell 0/0 because that is undefined. That is the reason why you cannot apply the algorithm to zero rational expressions, and so "nonzero" is specified in the algorithm.