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Chapter 0: Problem 75

Explain how to add or subtract rational expressions with the same denominators.

Short Answer

Expert verified
When adding or subtracting rational expressions with the same denominator, you add or subtract the numerators and keep the denominator the same, then simplify the final result, if possible.

Step by step solution

01

Understand the properties of fractions

Rational expressions are similar to fractions, and similar rules apply. Recall that when fractions have the same denominators, their numerators can be added or subtracted directly, while the denominator remains the same.
02

Use the fraction properties to solve rational expressions

Consider two rational expressions with the same denominators, for example \(\frac{a}{b}\) and \(\frac{c}{b}\). To add these rational expressions, simply add the numerators; that is, the solution would be \(\frac{a + c}{b}\). Similarly, to subtract these rational expressions, subtract the numerators to get \(\frac{a - c}{b}\).
03

Simplify the final rational expression (if possible)

After the addition or subtraction, the resulting rational expression might be simplified, if possible. This can be done usually by factoring both the numerator and the denominator and cancel out the common factors.

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