Rational Expressions

Math ⇒ Algebra

Rational Expressions starts at 8 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Rational Expressions. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 9

Add: \( \frac{1}{x} + \frac{2}{x^2} \)

Add: \( \frac{2}{x} + \frac{3}{x} \)

Add: \( \frac{2}{x+1} + \frac{3}{x+1} \)

Divide: \( \frac{5x}{6} \div \frac{10x}{9} \)

Divide: \( \frac{7y}{2} \div \frac{14y}{5} \)

Divide: \( \frac{8y}{3} \div \frac{16y}{9} \)

Multiply: \( \frac{2x}{3} \times \frac{9}{4x} \)

Multiply: \( \frac{3x}{4} \times \frac{8}{9x} \)

Which of the following is a necessary condition for a rational expression to be defined? (1) The numerator is not zero. (2) The denominator is not zero. (3) Both numerator and denominator are not zero. (4) The denominator is positive.

Which of the following is a rational expression? (1) \( \frac{2x}{x^2+1} \) (2) \( \sqrt{x+2} \) (3) \( x^3+1 \) (4) \( \frac{1}{x-1} \)

Which of the following is a rational expression? (1) \( \frac{x+2}{x-3} \) (2) \( \sqrt{x+1} \) (3) \( x^2 + 5 \) (4) \( \frac{2}{y} \)

Which of the following is equivalent to \( \frac{x^2-1}{x+1} \)? (1) \( x-1 \) (2) \( x+1 \) (3) \( x^2+1 \) (4) \( x-1 \)

A rational expression is defined as a fraction where the numerator and denominator are both ________.

A rational expression is undefined when its denominator is ________.

Fill in the blank: The denominator of a rational expression cannot be ________.

If \( \frac{a}{b} = \frac{c}{d} \), then \( a \times d = \underline{\hspace{1cm}} \times b \).

True or False: The expression \( \frac{2x+1}{x^2-4} \) is undefined for \( x = 2 \) and \( x = -2 \).

True or False: The product of two rational expressions is always a rational expression.

True or False: The quotient of two rational expressions is always a rational expression, provided the divisor is not zero.

True or False: The sum of two rational expressions is always a rational expression.