Questions: Given (5x+1)/((x-1)(x-2)) = a/(x-1) + 11/(x-2), then the value of a is

△ Determine the value of \( a \) in the given equation. ○ Combine fractions ▷ Combine the right side fractions using a common denominator. ☼ \(\frac{a}{x-1} + \frac{11}{x-2} = \frac{a(x-2) + 11(x-1)}{(x-1)(x-2)}\). The common denominator is \((x-1)(x-2)\). ○ Equate numerators ▷ Set the numerators equal since the denominators are the same. ☼ \(5x + 1 = a(x-2) + 11(x-1)\). Equating numerators gives \(5x + 1 = ax - 2a + 11x - 11\). ○ Solve for \( a \) ▷ Equate coefficients of \( x \) and constant terms to solve for \( a \). ☼ \(5 = a + 11\) and \(1 = -2a - 11\). Solving \(5 = a + 11\) gives \(a = -6\). Verification with \(1 = -2(-6) - 11\) confirms \(a = -6\). ✧ The value of \( a \) is \(-6\). ☺ The value of $a$ is -6.