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# Restrictions on Reducing to Lowest Terms

Reduce to lowest terms.

(w^2 − 49) / (w + 7)

The given expression is called a rational expression because both numerator and denominator are polynomials. A rational expression is not defined for those values of the variable that make the denominator 0. Thus, the expression (w^2 – 49)/(w + 7) is defined only when w + 7 ≠ 0, that is, when w ≠ -7.

To simplify a rational expression, we attempt to factorize the numerator and the denominator so that common factors, if any, can be canceled.

Now, w^2 – 49 = w^2 – 7^2 = (w + 7)(w – 7)
∴ (w^2 – 49)/(w + 7) = [(w + 7)(w – 7)]/(w + 7)
= w – 7 [Canceling the common (w + 7) term]
Thus, the given expression simplifies to w – 7 and this is the answer.

Why do you think the expression is undefined when w = -7? Why is zero in the denominator a
problem?

#### Solution Preview

We already know that (w^2 - 49)/(w + 7) = [(w - 7)(w + 7)]/(w + 7) = w - 7

The rational expression ...

#### Solution Summary

This solution explains the restriction this case of polynomial reduction in 83 words.

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