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Chapter 7: Problem 36

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{6 y+18}{11 y+33}$$

Short Answer

Expert verified
The simplified form of \(\frac{6y + 18}{11y + 33}\) is \(\frac{6}{11}\)

Step by step solution

01

Factor out common term from numerator and denominator

First, look for a common term in the numerator and denominator of the given expression. In the numerator, \(6 y + 18\), the common term is 6. After factoring out 6, the numerator becomes \(6(y + 3)\). In the denominator, \(11 y + 33\), the common term is 11. After factoring out 11, the denominator becomes \(11(y + 3)\). Therefore, the rational expression is now written as \(\frac{6(y + 3)}{11(y + 3)}\).
02

Simplify the expression

Notice that \(y + 3\) is a common factor in the numerator and the denominator. Cancelling out this common factor, the simplified rational expression becomes: \(\frac{6}{11}\)

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Most popular questions from this chapter

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{6 x+7}{x-6}+\frac{3 x}{6-x}$$

Explain how to subtract rational expressions when denominators are the same. Give an example with your explanation.

Factor completely: \(81 x^{4}-1\)

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{6}{x-5}+\frac{2}{5-x}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{3}{x}+\frac{4}{x-6}$$
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