Quick Answer
A rational expression is a fraction where both the numerator and denominator are polynomials. On the Digital SAT, these concepts typically appear in the Passport to Advanced Math section. Students frequently encounter these in approximately 2 to 4 questions per test, often requiring simplification or finding excluded values for the variable.
A rational expression is an algebraic fraction of the form P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero. It represents a ratio of two polynomial functions and is undefined at any x-value that results in a zero denominator.
Simplify the expression: (x^2 - 9) / (x^2 + 5x + 6). Solution: Factor both parts: [(x - 3)(x + 3)] / [(x + 2)(x + 3)]. Cancel the common factor (x + 3). The simplified expression is (x - 3) / (x + 2), where x is not equal to -2 or -3.
Canceling terms across addition: Students often incorrectly cancel individual terms like 'x' in (x+5)/x, forgetting that only factors of the entire numerator and denominator can be canceled.
Ignoring domain restrictions: Forgetting that an expression is undefined when the denominator is zero, even if the factor causing that zero is canceled out during the simplification process.
Incorrect sign distribution: Failing to distribute a negative sign to every term in the numerator when subtracting two rational expressions with a common denominator.
Students targeting 750+ should know that the SAT often masks rational expression problems as 'equivalent expression' questions. If factoring seems impossible, you can sometimes substitute a small, easy integer for the variable in both the original expression and the answer choices to find a numerical match, provided the number does not make any denominator zero.
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