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Chapter 7: Problem 95

Explain how to simplify a rational expression.

Short Answer

Expert verified
A rational expression can be simplified by factorizing the numerator and denominator and then cancelling out any common factors. The simplified form is the result when no common factors exist in the numerator and the denominator.

Step by step solution

01

Identify the Rational Expression

First identify the rational expression that needs to be simplified. A rational expression, or algebraic fraction, in most general form can be written as \(\frac{P(x)}{Q(x)}\), where \(P(x)\) and \(Q(x)\) are polynomials.
02

Factor the Numerator and the Denominator

Factorize the polynomials in the numerator and the denominator. The process may involve pulling out common factors, grouping, or using a special factoring formula depending on the given polynomials.
03

Cancel Common Factors

Upon successful factorization, look for any common factors that appear in both the numerator and the denominator. Cancel these out to simplify the expression. Remember, this can only be done if the common factor is multiplied by the entire numerator and the entire denominator.
04

Write the Simplified Expression

After cancelling out the common factors, rewrite the expression. This will be the simplified form of the rational expression.

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Most popular questions from this chapter

Add or subtract as indicated. Simplify the result, if possible. $$\frac{2}{y+5}+\frac{3}{4 y}$$

The temperature, in degrees Fahrenheit, of a dessert placed in a freezer for \(t\) hours is modeled by $$ \frac{t+30}{t^{2}+4 t+1}-\frac{t-50}{t^{2}+4 t+1} $$ a. Express the temperature as a single rational expression. b. Use your rational expression from part (a) to find the temperature of the dessert, to the nearest hundredth of a degree, after 1 hour and after 2 hours.

Graph: \(y=-\frac{2}{3} x+4 .\) (Section 3.4, Example 3)

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{3-x}{x-7}-\frac{2 x-5}{7-x}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{4-x}{x-9}-\frac{3 x-8}{9-x}$$
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