Rational Expressions
Math ⇒ Algebra
Rational Expressions starts at 8 and continues till grade 12.
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See sample questions for grade 12
Add the rational expressions: \( \frac{1}{x} + \frac{2}{x+1} \)
Divide: \( \frac{2x}{x^2-1} \div \frac{x}{x+1} \)
Find all values of \( x \) for which the rational expression \( \frac{2x+5}{x^2-4} \) is undefined.
Find the value of \( x \) if \( \frac{x+2}{x-1} = 3 \).
Given the rational expression \( \frac{4x}{x^2-4} \), what are its restrictions?
If \( \frac{2x}{x+1} = 4 \), find x.
If \( \frac{2x+3}{x-1} = 5 \), find x.
Multiply: \( \frac{x+2}{x-3} \times \frac{x-3}{x+5} \)
Given the rational expression \( \frac{4x}{x^2-4} \), what are its restrictions?
Which of the following is a rational expression? (1) \( \frac{x^2 + 1}{x - 3} \) (2) \( \sqrt{x} + 2 \) (3) \( \frac{2x}{x^2 - 4} \) (4) \( x^3 + 5 \)
Which of the following is equivalent to \( \frac{1}{x} + \frac{1}{y} \)? (1) \( \frac{x+y}{xy} \) (2) \( \frac{1}{x+y} \) (3) \( \frac{xy}{x+y} \) (4) \( \frac{1}{xy} \)
Which of the following is NOT a rational expression? (1) \( \frac{1}{x} \) (2) \( \frac{x^2+1}{x-2} \) (3) \( \sqrt{x} \) (4) \( \frac{2x}{x^2+1} \)
Which of the following is the correct simplified form of \( \frac{x^2-1}{x+1} \)? (1) x-1 (2) x+1 (3) x^2+1 (4) x-1/x+1
A rational expression is defined as a ratio of two _________.
The rational expression \( \frac{1}{x-5} \) is undefined for x = _______.
The rational expression \( \frac{2x+1}{x^2-1} \) is undefined for x = _______ and x = _______.
A rational expression can have more than one restriction on its domain. True or False?
A rational expression is always defined for all real numbers. True or False?
If \( \frac{a}{b} = \frac{c}{d} \), then \( \frac{a}{c} = \frac{b}{d} \). True or False?
If \( \frac{a}{b} = \frac{c}{d} \), then \( \frac{a+b}{b} = 1 + \frac{c}{d} \). Yes or No?
