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Chapter 0: Problem 11

Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$\frac{y^{2}+7 y-18}{y^{2}-3 y+2}$$

Short Answer

Expert verified
The simplified expression is \(\frac{y + 9}{y - 1}\) and the number that must be excluded from the domain is \(1\).

Step by step solution

01

Factoring The Numerator and The Denominator

The numerator is factored to \((y - 2)(y + 9)\) and the denominator is factored to \((y - 1)(y - 2)\). The rational function thus becomes \(\frac{(y - 2)(y + 9)}{(y - 1)(y - 2)}\)
02

Simplify The Rational Expression

Since \(y-2\) appears in both the numerator and the denominator, it can be cancelled out. Hence, the simplified expression will be \(\frac{y + 9}{y - 1}\).
03

Finding The Excluded Values

The values that must be excluded from the domain are those that make the denominator zero. Equating \(y-1\) to zero gives \(y=1\) . Therefore, \(1\) must be excluded from the domain.

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Most popular questions from this chapter

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