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
Hey birajlimbu848 — ready when you are. Here are the solutions to the problems: 1. Simplify: (1)/(1+x^2) + (2)/(1+x^2) - (4)/(1-x^4) Step 1: Combine the first two terms since they have the same denominator. (1+2)/(1+x^2) - (4)/(1-x^4) = (3)/(1+x^2) - (4)/(1-x^4) Step 2: Factor the denominator of the second term using the difference of squares formula, A^2-B^2 = (A-B)(A+B). Here, 1-x^4 = (1-x^2)(1+x^2). (3)/(1+x^2) - (4)/((1-x^2)(1+x^2)) Step 3: Find the common denominator, which is (1-x^2)(1+x^2). Multiply the numerator and denominator of the first term by (1-x^2). (3(1-x^2))/((1-x^2)(1+x^2)) - (4)/((1-x^2)(1+x^2)) Step 4: Combine the numerators and simplify. (3(1-x^2) - 4)/((1-x^2)(1+x^2)) = (3-3x^2-4)/(1-x^4) = (-1-3x^2)/(1-x^4) = (-(1+3x^2))/(1-x^4) 2. Simplify: $(a-b)/(a^2-ab+b^2) + (a+b)/(a^2+ab+b^2) - 2b^3a^4+a