Multiplying and dividing rational expressions 1 | Algebra II | Khan Academy | Summary and Q&A

TL;DR

Simplify a rational expression by multiplying the numerator and the denominator, and state the domain as all real numbers except for 0.

Key Insights

• 😑 The domain of a rational expression is all real numbers except for 0, as any value that makes the denominator 0 will result in an undefined expression.
• ✖️ Multiplying a rational expression involves multiplying the numerators and denominators separately.
• 😑 It is important to simplify rational expressions to make them easier to work with and compare.
• 😑 Common factors in a rational expression can be canceled out to further simplify the expression.
• 😑 The simplified form of a rational expression should have the same domain as the original expression.
• 😑 Constraints on the domain can result in fundamentally different expressions.
• 🧑‍🏭 The simplification process involves dividing common factors and simplifying fractions.

Transcript

Multiply and express as a simplified rational. State the domain. We'll start with the domain. The only numbers that will make this expression undefined are the ones that would make the denominator equal to 0, and those are the situation, or that situation would occur, when either a, b, x, or y is equal to 0. If any of those are equal to 0, then we ... Read More

Questions & Answers

Q: What is the domain of a rational expression?

The domain of a rational expression is all real numbers except for 0. If the denominator is equal to 0, the expression becomes undefined.

Q: How do you simplify a rational expression?

To simplify a rational expression, multiply the numerator and denominator. Then, simplify any common factors in the resulting expression by canceling out common factors.

Q: Can the domain of a rational expression impact its simplified form?

Yes, the domain of a rational expression can impact its simplified form. If certain values are not allowed in the domain, they need to be excluded from the simplified expression as well.

Q: Why do we simplify rational expressions?

Simplifying rational expressions makes them easier to work with and understand. It allows for easier manipulation and comparison of different expressions.

Summary & Key Takeaways

• The domain of a rational expression is all real numbers except for 0, as any value that makes the denominator 0 will result in an undefined expression.

• To simplify a rational expression, multiply the numerator and denominator, and simplify any common factors.

• The simplified rational expression will have a simplified numerator and denominator that can be further simplified if possible.