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If (x^4)/((x-1)(x-2))=(16)/(x-2)-(1)/(x-...

If `(x^4)/((x-1)(x-2))=(16)/(x-2)-(1)/(x-1)+x^(2)+3 x+k` ,then `k=`

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To solve the equation \[ \frac{x^4}{(x-1)(x-2)} = \frac{16}{x-2} - \frac{1}{x-1} + x^2 + 3x + k, \] we need to find the value of \( k \). ### Step 1: Find a common denominator for the right-hand side The common denominator for the terms on the right-hand side is \( (x-1)(x-2) \). So, we can rewrite the right-hand side as: \[ \frac{16(x-1)}{(x-2)(x-1)} - \frac{1(x-2)}{(x-1)(x-2)} + (x^2 + 3x + k)(x-1)(x-2). \]
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