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Chapter 0: Problem 101

Explain how to divide rational expressions.

Short Answer

Expert verified
To divide rational expressions: firstly, simplify them. Then, replace the division operation with multiplication by the reciprocal. Finally, you multiply straight across numerators and denominators separately and simplify the result.

Step by step solution

01

Simplify the Expressions

If the rational expressions have any factors in common, they must be simplified. This means factoring both the numerator and denominator of each fraction (if possible) and cancelling any common factors. Given \( \frac{a}{b} 梅 \frac{c}{d} \), simplify \( \frac{a}{b} \) and \( \frac{c}{d} \) separately by factoring.
02

Take the Reciprocal

Division is the same as multiplication by the reciprocal, so change the operation from division to multiplication and take the reciprocal of second fraction. In other words, flip the second fraction. \( \frac{a}{b} 梅 \frac{c}{d} \) becomes \( \frac{a}{b} * \frac{d}{c} \).
03

Multiply

Now that you have two fractions you are multiplying, simply multiply straight across. Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. The result is \( \frac{ad}{bc} \).
04

Simplify the Result

If the resulting fraction can be simplified further, do so by factoring the numerator and denominator and cancelling any common terms.

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Most popular questions from this chapter

List all numbers that must be excluded from the domain of each rational expression. $$\frac{3}{2 x^{2}+4 x-9}$$

How is the quadratic formula derived?

Describe ways in which solving a linear inequality is different than solving a linear equation.

Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. $$\frac{x^{2}+6 x+5}{x^{2}-25}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I factored \(4 x^{2}-100\) completely and obtained \((2 x+10)(2 x-10)\).
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