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Chapter 7: Problem 22

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{9 x^{2}}{6 x}$$

Short Answer

Expert verified
The simplified form of \( \frac{9x^{2}}{6x} \) is \( \frac{3x}{2} \).

Step by step solution

01

Identify common factors

Look at the numerator and the denominator and find common factors. Both \(9x^{2}\) and \(6x\) are divisible by \(3x\).
02

Simplify by cancelling out common factors

Divide the numerator and the denominator by the common factor. This makes \(9x^{2}\) to be reduced to \(3x\) and \(6x\) to be reduced to \(2\). The simplified expression is \(\frac{3x}{2}\).

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Most popular questions from this chapter

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can solve \(\frac{x}{9}=\frac{4}{6}\) by using the cross-products principle or by multiplying both sides by \(18,\) the least common denominator.

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{3 x}{(x+1)^{2}}-\left[\frac{5 x+1}{(x+1)^{2}}-\frac{3 x+2}{(x+1)^{2}}\right]$$

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

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x^{2}}{x-2}+\frac{4}{2-x}$$

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