Advanced Math practice question

Answer: A. (x + 3) / ((x − 1)(x + 1))

Common denominator (x − 1)(x + 1). Rewrite: 2(x + 1)/((x − 1)(x + 1)) − (x − 1)/((x − 1)(x + 1)). Subtract numerators: 2x + 2 − x + 1 = x + 3.

Why the other answers are wrong

B. 1 / ((x − 1)(x + 1))

The numerators 2 and 1 were subtracted without first rewriting each fraction over the common denominator.

C. (x − 3) / ((x − 1)(x + 1))

A sign slipped when subtracting (x − 1): 2x + 2 − x + 1 is x + 3, not x − 3. Subtracting a bracket flips both its signs.

D. (3x + 1) / ((x − 1)(x + 1))

3x + 1 comes from ADDING the rewritten numerators, 2(x + 1) + (x − 1). The second fraction is subtracted.

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…