Rational Expressions
Math ⇒ Algebra
Rational Expressions starts at 8 and continues till grade 12.
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See sample questions for grade 11
Add the rational expressions: 1/(x + 1) + 2/(x - 1).
Divide: (2x)/(x² - 1) ÷ (x)/(x + 1).
Divide: (x² - 1)/(x + 1) ÷ (x - 1)/(x + 2).
Explain the process of simplifying a complex rational expression.
Explain why the rational expression (x² - 1)/(x - 1) is not defined for x = 1.
Given the rational expression (x² - 4x + 3)/(x² - 9), list all values of x for which the expression is undefined.
If f(x) = (x² - 4)/(x + 2), what is the value of f(-2)?
Given the context: A rational function models the speed of a car as \( v(t) = \frac{100t}{t^2 + 25} \), where t is time in seconds. What is the maximum possible speed as t increases without bound?
Which of the following is a rational expression? (1) x + 2 (2) (x² + 1)/(x - 3) (3) √x + 1 (4) sin(x)/x
Which of the following is NOT a rational expression? (1) (x² + 1)/(x - 1) (2) (x + 2)/√x (3) (x³ - 8)/(x² + 4x + 4) (4) (2x + 1)/(x² + 1)
Which of the following is the correct simplified form of (x² - 9x + 18)/(x - 3)? (1) x - 6 (2) x + 6 (3) x - 3 (4) x + 3
Which of the following values of x makes the rational expression (x + 2)/(x² - 4) undefined? (1) x = 2 (2) x = -2 (3) x = 0 (4) Both 1 and 2
A rational expression is defined as the ratio of two _________.
Fill in the blank: The expression (x² + 3x + 2)/(x + 1) simplifies to _________.
Fill in the blank: The lowest common denominator (LCD) of 1/(x + 2) and 1/(x - 2) is _________.
A rational expression is called proper if the degree of the numerator is _______ than the degree of the denominator.
True or False: The expression (x² + 1)/(x - 2) is undefined when x = 2.
True or False: The product of two rational expressions is always a rational expression.
True or False: The rational expression (x² + 1)/(x² + 1) is equal to 1 for all real values of x.
True or False: The sum of two rational expressions is always a rational expression.
