Subtracting rational expressions | Polynomial and rational functions | Algebra II | Khan Academy

TL;DR

Learn how to subtract rational expressions by finding a common denominator and simplifying the result.

Transcript

We're asked to subtract and state the difference in simplest form. So we're subtracting one rational expression from another. And just like the case when you are subtracting fractions, or adding fractions for that matter, you have to make sure that you have a common denomintator. And over here it looks like we have kind of the same components, but ... Read More

Key Insights

• 😑 Subtraction of rational expressions requires finding a common denominator.
• ❓ The least common multiple (LCM) is used to determine the common denominator.
• 😑 By multiplying the numerators and denominators by the necessary factors, the expressions can be subtracted.
• 😑 Simplifying the resulting expression involves combining like terms and dividing the numerator and denominator by common factors.
• 😑 Understanding how to simplify rational expressions is crucial for solving algebraic equations efficiently.
• 😑 Subtraction of rational expressions follows the same principles as subtracting fractions.
• ❓ The process may seem complex, but once the common denominator is found, the steps become straightforward.

Questions & Answers

Q: How do you subtract rational expressions?

To subtract rational expressions, first find a common denominator by determining the least common multiple of the denominators. Then, multiply each rational expression by the necessary factors to obtain the common denominator. Finally, subtract the numerators and simplify the result.

Q: Why is it important to find a common denominator?

Finding a common denominator is essential when subtracting rational expressions because it allows us to combine them effectively. Without a common denominator, the expressions cannot be directly subtracted.

Q: How do you determine the least common multiple of the denominators?

To find the least common multiple (LCM) of the denominators, factor each denominator into its prime components and multiply the highest power of each prime factor. The product represents the LCM of the denominators.

Q: What step should be taken after subtracting the numerators?

After subtracting the numerators, simplify the resulting expression by combining like terms. Also, check if the numerator and denominator have any common factors and divide them to express the final result in simplest form.

Summary & Key Takeaways

• To subtract rational expressions, find a common denominator by determining the least common multiple of the denominators.

• Multiply both the numerator and denominator of each rational expression by the necessary factors to obtain the common denominator.

• Simplify the resulting expression by combining like terms and dividing both the numerator and denominator by any common factors.