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
Alright IT — let's do this. The problem asks to show that e^-xe^-x+1 = (1)/(e^x+1). Step 1: Start with the left-hand side (LHS) of the equation. LHS = e^-xe^-x+1 Step 2: To eliminate the negative exponent e^-x from the expression, multiply both the numerator and the denominator by e^x. LHS = e^-x · e^x(e^-x+1) · e^x Step 3: Simplify the numerator and distribute e^x in the denominator. Recall that e^-x · e^x = e^-x+x = e^0 = 1. LHS = (1)/(e^-x) · e^x + 1 · e^x LHS = (1)/(e^0 + e^x) LHS = (1)/(1 + e^x) Step 4: Rearrange the terms in the denominator to match the right-hand side (RHS) of the original equation. LHS = (1)/(e^x + 1) This is equal to the RHS. Therefore, the identity is shown. Shown: e^-xe^-x+1 = (1)/(e^x+1) Send me the next one 📸