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: Find a common denominator for the two fractions. The common denominator is 6(x-5). Step 2: Rewrite each fraction with the common denominator. (x-5)/(6) - (6)/(x-5) = ((x-5)(x-5))/(6(x-5)) - (6 × 6)/(6(x-5)) = ((x-5)^2)/(6(x-5)) - (36)/(6(x-5)) Step 3: Combine the fractions by subtracting the numerators. = ((x-5)^2 - 36)/(6(x-5)) Step 4: Expand the numerator and simplify. Recall that (a-b)^2 = a^2 - 2ab + b^2. (x-5)^2 = x^2 - 2(x)(5) + 5^2 = x^2 - 10x + 25 Substitute this back into the numerator: (x^2 - 10x + 25 - 36)/(6(x-5)) = (x^2 - 10x - 11)/(6(x-5)) The simplified expression is: (x^2 - 10x - 11)/(6(x-5)) Drop the next question.