Advanced MathVery hardCombining two rational expressions
Advanced Math practice question
For x ≠ 1 and x ≠ −1, the expression 1/(x − 1) − 1/(x + 1) is equivalent to k/(x² − 1), where k is a constant. What is the value of k?
Answer: 2
Common denominator (x − 1)(x + 1) = x² − 1: the numerator is (x + 1) − (x − 1) = 2.
Common wrong answers
- If you answered 0
- 0 forgets that subtracting (x − 1) flips the sign of −1.
- If you answered -2
- −2 subtracts in the wrong order.
- If you answered 2x
- The x terms cancel; the numerator is a constant.
More Advanced Math questions
- Very hard
The function f(x) = x² + 6x + 5 is rewritten in the form f(x) = (x + a)² + b. What is the value of b? - Very hard
What is the solution to the equation 6/(x − 2) = 3? - Very hard
The polynomial p(x) = x³ − 4x has how many distinct real zeros? - Very hard
The polynomial p is defined by p(x) = x³ + ax² + bx − 12, where a and b are constants. If x − 2 is a factor of… - Very hard
The function f, defined by f(x) = 3000(1.331)^(x/12), gives the value, in dollars, of an investment x months a… - Very hard
In the xy-plane, the parabola y = x² − 4x + 7 and the line y = mx − 2, where m is a constant, intersect at exa…
Not affiliated with the College Board. SAT is a trademark of the College Board.