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
Step 1: Perform polynomial long division of the numerator by the denominator. We want to divide 2x^3 - x by x^2 - 1. c|cc cc 2r2x \\ 2-5 x^2 - 1 & 2x^3 & +0x^2 & -x \\ 2r-(2x^3 & & -2x) \\ 2-4 2r0 & & x \\ The quotient is 2x and the remainder is x. Step 2: Write the function in the form of quotient plus remainder over divisor. This means f(x) = quotient + remainderdivisor. f(x) = 2x + (x)/(x^2 - 1) Step 3: Identify g(x) and h(x). Comparing this to the form g(x) + h(x), we have: g(x) = 2x h(x) = (x)/(x^2 - 1) The function f(x) expressed in the form g(x) + h(x) is: 2x + (x)/(x^2 - 1) Send me the next one 📸