How to Subtract Rational Expressions Step by Step

TL;DR

To subtract rational expressions, first find a common denominator by factoring both denominators. Adjust the numerators accordingly, then combine them and simplify. The domain of the resulting expression includes all real numbers except for any value that makes the denominator zero.

Transcript

Find the difference. Express the answer as a simplified rational expression, and state the domain. We have two rational expressions, and we're subtracting one from the other. Just like when we first learned to subtract fractions, or add fractions, we have to find a common denominator. The best way to find a common denominator, if were just dealing ... Read More

Key Insights

• 😑 Factoring the denominators allows us to find a common denominator when subtracting rational expressions.
• 🧑‍🏭 Multiplying the numerator and denominator by a common factor ensures that the denominators are the same.
• 😑 The domain of a rational expression is all real numbers except for the value that makes the denominator equal to zero.
• 😑 Simplifying the rational expression involves combining like terms in the numerator.

Questions & Answers

Q: How do you find a common denominator when subtracting rational expressions?

To find a common denominator, factor each denominator and ensure that the resulting denominator has all the factors of both denominators.

Q: What is the domain for the simplified rational expression?

The domain is all real numbers except for the value that makes the denominator equal to zero. In this case, the domain is all values of 'a' except for -2.

Q: Why do we multiply the numerator and denominator by a common factor?

By multiplying the numerator and denominator by a common factor, we ensure that the denominator is the same, allowing us to subtract the rational expressions.

Q: Can we simplify the numerator further?

If the numerator contains a common factor with the denominator, we can factor out that common factor. However, in this case, the numerator does not contain a common factor with the denominator, so no further simplification is possible.

Summary & Key Takeaways

• To subtract rational expressions, find a common denominator by factoring the denominators and combining them.

• Multiply the numerator and denominator by the necessary factors to create a common denominator.

• Simplify the expression by multiplying out the numerator and combining like terms. The domain is all real numbers except for the value that makes the denominator equal to zero.