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# Restrictions on Reducing to Lowest Terms

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Reduce to lowest terms.

(w^2 âˆ’ 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 â‰  0, that is, when w â‰  -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)
âˆ´ (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?

https://brainmass.com/math/basic-algebra/restrictions-reducing-lowest-terms-205667

#### Solution Preview

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

The rational ...

#### Solution Summary

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

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