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Chapter 0: Problem 72

Explain how to simplify a rational expression.

Short Answer

Expert verified
To simplify a rational expression, factorize the numerator and denominator, cancel out the common factors, then write down the simplified form of the expression.

Step by step solution

01

Factorize the Numerator and Denominator

Factor the numerator and the denominator of the rational expression. Factoring is a process that breaks down a polynomial into the product of simpler polynomials. In other words, this is about simplifying the polynomials in the fraction.
02

Identify Common Factors

Identify the common factors between the numerator and the denominator. A common factor refers to a term that is present both in the numerator and the denominator.
03

Cancel Common Factors

Cancel out the common factors from the numerator and the denominator. This is based on the fraction property that says \(\frac{a}{a}=1\). Thus, by cancelling the common factors, we simplify the rational expression.
04

Write the Simplified Form

Write down the result obtained after cancelling shared factors. If there are no more common factors in the numerator and denominator other than 1, the rational expression is simplified to its lowest terms.

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Most popular questions from this chapter

Use the product rule to simplify the expressions in Exercises \(7-16 .\) In Exercises \(11-16,\) assume that variables represent nonnegative real numbers. $$\sqrt{45 x^{2}}$$

Simplify each exponential expression $$ \left(\frac{3 x^{4}}{y}\right)^{-3} $$

Use the quotient rule to simplify the expressions in Exercises \(17-26 .\) Assume that \(x>0\) $$\sqrt{\frac{121}{9}}$$

Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$ \frac{x^{2}-12 x+36}{4 x-24} $$

Find all numbers that must be excluded from the domain of each rational expression. $$ \frac{x+5}{x^{2}-25} $$
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