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
Right Rajnish, let's go. Here's the solution for question 30 and 31. 30. Prove that (1)/( x - x) - (1)/( x) = (1)/( x) - (1)/( x + x) Step 1: Rearrange the terms to group similar expressions. Move the x + x term to the LHS and the x term to the RHS. (1)/( x - x) + (1)/( x + x) = (1)/( x) + (1)/( x) Step 2: Simplify the Right Hand Side (RHS). RHS = (2)/( x) Step 3: Work on the Left Hand Side (LHS). Find a common denominator for the two fractions. LHS = (( x + x) + ( x - x))/(( x - x)( x + x)) Step 4: Simplify the numerator and the denominator. The denominator is a difference of squares. LHS = x + x + x - x^2 x - \