This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — Step 1: Simplify the denominators of the given expression. The expression is: (1)/(((t^2-1)-1)) + (2)/(((t^2-1)+1)) Simplify the first denominator: (t^2-1)-1 = t^2-2 Simplify the second denominator: (t^2-1)+1 = t^2 Step 2: Rewrite the expression with the simplified denominators. (1)/(t^2-2) + (2)/(t^2) Step 3: Find a common denominator to combine the fractions. The common denominator is t^2(t^2-2). Multiply the first term by (t^2)/(t^2) and the second term by (t^2-2)/(t^2-2): (1)/(t^2-2) · (t^2)/(t^2) + (2)/(t^2) · (t^2-2)/(t^2-2) = (t^2)/(t^2(t^2-2)) + (2(t^2-2))/(t^2(t^2-2)) Step 4: Combine the numerators over the common denominator. = (t^2 + 2(t^2-2))/(t^2(t^2-2)) = (t^2 + 2t^2 - 4)/(t^2(t^2-2)) = (3t^2 - 4)/(t^2(t^2-2)) The simplified expression is (3t^2 - 4)/(t^2(t^2-2)). Drop the next question.