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Chapter 0: Problem 99

Explain how to simplify a rational expression.

Short Answer

Expert verified
To simplify a rational expression, it needs to be factorized and then cancel any common terms in the numerator and the denominator. The simplified form of our example rational expression \(\frac{2x^2 + 3x - 2}{x^2 - 1}\) is \(\frac{(2x-1)(x+2)}{(x-1)(x+1)}\)

Step by step solution

01

Identify the rational expression

First step is to identify the rational expression that needs to be simplified. Rational expressions are fractions in which both the numerator and the denominator are polynomials. For example, \(\frac{2x^2 + 3x - 2}{x^2 - 1}\) is a rational expression.
02

Factorize the numerator and denominator

Next step is to factorize both the numerator and the denominator. Factorization is breaking down the complicated terms into simpler terms that can be multiplied together to obtain original term. For example, the above expression can be factorized as: \(\frac{(2x-1)(x+2)}{(x-1)(x+1)}\)
03

Simplify the rational expression

Simplifying involves cancellation of common terms in the numerator and denominator, if any. However in the factorized form of above expression, there are no common terms to cancel out. Hence, the simplified form of the rational expression is \(\frac{(2x-1)(x+2)}{(x-1)(x+1)}\)

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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. Because I want to solve \(25 x^{2}-169=0\) fairly quickly, I'll use the quadratic formula.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$x^{2}+36=(x+6)^{2}$$

This will help you prepare for the material covered in the next section. Multiply and simplify: \(12\left(\frac{x+2}{4}-\frac{x-1}{3}\right)\).

This will help you prepare for the material covered in the next section. Evaluate $$\frac{-b-\sqrt{b^{2}-4 a c}}{2 a}$$ for \(a=2, b=9,\) and \(c=-5\)

Perform the indicated operations. Simplify the result, if possible. $$\left(2-\frac{6}{x+1}\right)\left(1+\frac{3}{x-2}\right)$$
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