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Adding and Subtracting Rational Expressions with Like Denominators

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Adding and Subtracting Rational Expressions with Like Denominators

Study Guide

Key Definition

Rational expressions are fractions where the numerator and denominator are polynomials. To add or subtract rational expressions with the same denominators, add or subtract the numerators and place the result over the common denominator.

Important Notes

Rational expressions can be simplified just like fractions.
Always ensure that the denominator is not equal to zero.
Addition and subtraction of rational expressions follow the same rules as addition and subtraction of fractions.

Mathematical Notation

$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$ represents adding rational expressions with the same denominator (c ≠ 0).

$\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$ represents subtracting rational expressions with the same denominator (c ≠ 0).

Remember to use proper notation when solving problems

Why It Works

Since the denominators are the same, they serve as a common 'container' for the numerators. Thus, we can add or subtract the numerators and put the result over the common denominator.

Remember

Always simplify your final expression and ensure the denominator is not zero.

Quick Reference

Addition:$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$ where c ≠ 0

Subtraction:$\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$ where c ≠ 0

Understanding Adding and Subtracting Rational Expressions with Like Denominators

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Adding or subtracting rational expressions with like denominators is just like adding or subtracting fractions. We simply add or subtract the numerators and put the result over the common denominator.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Add the rational expressions: $\frac{n}{n+3} + \frac{2n}{n+3}$.

Real-World Problem

Question Exercise

Intermediate

Paint Mixing Scenario

You are mixing two paint solutions: you need $\frac{3x}{x-1}$ liters of yellow paint and $\frac{2x}{x-1}$ liters of blue paint. How many liters of paint do you have in total? (x ≠ 1)

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Subtract the rational expressions: $\frac{1}{2-x} - \frac{4}{2-x}$.

Challenge Quiz

Single Choice Quiz

Advanced

Subtract the rational expressions: $\frac{x^2}{x^{2}-4} - \frac{4x}{x^{2}-4}$.

Recap

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Review key concepts and takeaways