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 denominators are 6 and x-5. The least common multiple (LCM) of these is 6(x-5). Step 2: Rewrite each fraction with the common denominator. (x-5)/(6) = ((x-5)(x-5))/(6(x-5)) = ((x-5)^2)/(6(x-5)) (6)/(x-5) = (6 × 6)/(6(x-5)) = (36)/(6(x-5)) Step 3: Subtract the rewritten fractions. ((x-5)^2)/(6(x-5)) - (36)/(6(x-5)) = ((x-5)^2 - 36)/(6(x-5)) Step 4: Expand the numerator and simplify. Recognize that (x-5)^2 - 36 is a difference of squares, a^2 - b^2 = (a-b)(a+b), where a = (x-5) and b = 6. (x-5)^2 - 36 = ((x-5) - 6)((x-5) + 6) = (x-5-6)(x-5+6) = (x-11)(x+1) Step 5: Substitute the simplified numerator back into the expression. ((x-11)(x+1))/(6(x-5)) The simplified expression is: ((x-11)(x+1))/(6(x-5)) Drop the next question.