1.4 Rational Expressions
Ideas in this lesson
- Domain of an algebraic expression
- Simplifying rational expressions
- Multiplying and dividing rational expressions
- Adding and subtracting rational expressions
- Compound fractions
- Rationalizing a denominator or numerator
- Avoiding common algebra errors
- Simplify structured quotients and radical combinations
- Interpret and evaluate rational models
- Investigate excluded inputs and prove bounds
Domain of an algebraic expression · Worked example
Find the real domain of \(\dfrac{1}{\sqrt{x-5}}\).
Answer: \((5,\infty)\)
The radicand must be nonnegative for a real square root.
Because the square root is also in the denominator, it cannot equal zero.
Therefore \(x-5>0\), so the domain is \((5,\infty)\).
Because the square root is also in the denominator, it cannot equal zero.
Therefore \(x-5>0\), so the domain is \((5,\infty)\).