Question : Simplify the following expression.
$\{[(x-5)(x-1)]-[(9 x-5)(9x-1)]\} \div 16x$
Option 1: $2x(5x-3)$
Option 2: $-(5x-3)$
Option 3: $x(5x-3)$
Option 4: $-6x(5x-3)$
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Correct Answer: $-(5x-3)$
Solution :
Given: $\{[(x-5)(x-1)]-[(9 x-5)(9x-1)]\} \div 16x$
$= [(x^{2}-x-5x+5)-[(81x^{2}-9x-45x+5)]\div 16x$
$= [(x^{2}-6x+5)-[(81x^{2}-54x+5)]\div 16x$
$= [(x^{2}-6x+5-81x^{2}+54x-5)]\div 16x$
$= [-80x^{2}+48x]\div 16x$
$=[-5x+3]$
$=-(5x-3)$
Hence, the correct answer is $-(5x-3)$.
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