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: Factor the numerator. The numerator is 2x+14. Factor out the common factor of 2: 2x+14 = 2(x+7) Step 2: Factor the denominator. The denominator is 2x^2-98. First, factor out the common factor of 2: 2x^2-98 = 2(x^2-49) Recognize that x^2-49 is a difference of squares, a^2-b^2 = (a-b)(a+b), where a=x and b=7: x^2-49 = (x-7)(x+7) So, the fully factored denominator is: 2(x-7)(x+7) Step 3: Rewrite the expression with the factored numerator and denominator. (2(x+7))/(2(x-7)(x+7)) Step 4: Cancel out common factors from the numerator and denominator. Both the numerator and the denominator have factors of 2 and (x+7). 2(x+7)2(x-7)(x+7) = (1)/(x-7) The simplified expression is: (1)/(x-7) Drop the next question!