154k views
3 votes
Simplify the rational expression and find the excluded values.
x²-x/(x - 1)(x + 7).

User Aetodd
by
8.8k points

1 Answer

3 votes

Final answer:

The simplified expression is x/(x + 7), after factoring and canceling out the common (x - 1) term in the numerator and denominator. Excluded values are x = 1 and x = -7 because they make the original denominator zero.

Step-by-step explanation:

To simplify the rational expression x² - x over (x - 1)(x + 7) we must first factor the numerator. We can factor out an x to get x(x - 1).

Now, the expression looks like this: x(x - 1) over (x - 1)(x + 7). We see that (x - 1) is a common factor in both the numerator and the denominator, so we can eliminate it.

Simplifying this we get x over (x + 7). However, we must also determine the excluded values. These are the values of x that would make the original denominator equal to zero, which are x = 1 and x = -7. Thus, the simplified expression is x/(x + 7) with excluded values of 1 and -7.

To check that this is reasonable, we can plug in a value for x (other than 1 and -7) into both the original and simplified expressions to ensure they produce the same result. Doing this with x = 2, for example, would give the same result for both, confirming the simplification is correct.

User Leo Ma
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories