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Chapter 8: Problem 2

When adding or subtracting two rational expressions, do you keep the LCD throughout the problem or do you eliminate the denominators?

Short Answer

Expert verified
When adding or subtracting two rational expressions, you should keep the LCD throughout the problem and not eliminate the denominators. However, after combining the numerators, you may need to simplify the resulting expression if the numerator and denominator share a common factor.

Step by step solution

01

Understand Rational Expressions

A rational expression is a fraction where the numerator and the denominator are both polynomials. When adding or subtracting two rational expressions, the goal is to combine the expressions into a single fraction with the same denominators.
02

Find the Least Common Denominator (LCD)

In order to add or subtract two fractions, we first need to find a common denominator for both expressions. The LCD is the smallest multiple of all the denominators, so we need to find the Least Common Multiple (LCM) of the denominators of the expressions.
03

Rewrite the fractions with the LCD

Once the LCD is found, rewrite each fraction such that the denominator is the LCD. Depending on the original denominators, you might need to multiply the numerator and the denominator of each fraction by the appropriate factors to make the denominators equal to the LCD.
04

Add or subtract the rational expressions

After rewriting the fractions with the LCD as their denominators, you can add or subtract the numerators according to the given problem. The denominator should remain the same (LCD) while combining the numerators.
05

Simplify the result

After adding or subtracting the numerators, the resulting expression might need to be simplified, especially if the numerator and the denominator share a common factor. If so, divide both the numerator and the denominator by the common factor to simplify the expression. However, the denominator should not be eliminated entirely, as it is still part of the rational expression. To conclude, when adding or subtracting two rational expressions, we keep the LCD throughout the problem and do not eliminate the denominators. However, it is essential to simplify the resulting expression after adding or subtracting the rational expressions.

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Most popular questions from this chapter

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