Answer these 10 multiple-choice questions on excluded values, simplifying, operations, rational equations, extraneous solutions, and work problems. Each question has exactly one correct answer, and the explanation after it names the key step.
For which values of \(x\) is \(\frac{x+2}{x^{2}-25}\) undefined?
Simplify \(\frac{x^{2}-9}{x^{2}-6x+9}\).
Multiply and simplify: \(\frac{x}{x+2}\cdot\frac{x+2}{x-5}\).
What is the LCD of \(\frac{1}{x^{2}-4}\) and \(\frac{1}{x+2}\)?
Solve \(\frac{4}{x+1}=\frac{2}{x}\).
The graph is the line \(y=x+2\) with a hole at \((3,5)\). Which expression has this graph?
The graphs show both sides of \(\frac{x}{x-3}=\frac{3}{x-3}\). How many solutions does the equation have?
Pipe A fills a tank in \(3\) hours and pipe B fills it in \(6\) hours. How long do they take together?
Rewrite \(\frac{x+5}{x+2}\) as a constant plus a fraction.
Add: \(\frac{1}{x}+\frac{1}{x+1}\).
🎉 Quiz complete!
Remember:
- Standards A-APR.D.6, A-APR.D.7, and A-REI.A.2: rewrite, operate on, and solve with rational expressions.
- Excluded values are the zeros of the denominator, and they remain even after canceling.
- Dividing means multiplying by the reciprocal; adding needs a common denominator.
- Always check solutions of a rational equation: an extraneous solution makes a denominator zero.
- Work problems add rates: \(\frac{1}{a}+\frac{1}{b}=\frac{1}{t}\).
See every chapter on the Algebra 2 math page.