Problem 53
Question
What is a complex rational expression? Give an example with your explanation.
Step-by-Step Solution
Verified Answer
A complex rational expression is a rational expression where the numerator and / or the denominator are also rational expressions. Example: \(\frac{\frac{5}{x} + 3}{1 - \frac{2}{x}}\).
1Step 1: Defining Complex Rational Expression
A complex rational expression is a fraction where the numerator and / or the denominator are also fractions. They can be thought of as a fraction divided by another fraction or multiple fractions. It extends the idea of rational numbers (which are simply fractions) to expressions that contain polynomials.
2Step 2: Example of Complex Rational Expression
Consider an example of a complex rational expression: \(\frac{\frac{5}{x} + 3}{1 - \frac{2}{x}}\). This is a complex rational expression because the numerator \(\frac{5}{x} + 3\) and the denominator \(1 - \frac{2}{x}\) both contain rational expressions or fractions.
Other exercises in this chapter
Problem 53
Factor: \(25 x^{2}-81 .\) (Section 6.4, Example 1)
View solution Problem 53
Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{(x-4)^{2}}{x^{2}-16}$$
View solution Problem 53
Add or subtract as indicated. Simplify the result, if possible. $$\frac{3 x}{x^{2}+3 x-10}-\frac{2 x}{x^{2}+x-6}$$
View solution Problem 53
Divide as indicated. $$\frac{y^{3}+y}{y^{2}-y} \div \frac{y^{3}-y^{2}}{y^{2}-2 y+1}$$
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