Question

Determine whether the following equation has roots 1÷x+1+2÷x+2=4÷x+4

Answer 1

$\frac{1}{x} +1 + \frac{2}{x} + 2 = \frac{4}{x} + 4$

$\frac{1 + x + 2 + 2x}{x} = \frac{4 + 4x}{x} \\ \\ x(3x + 3) = x(4 + 4x) \\ \\ \frac{x(3x + 3)}{x} = 4 + 4x$
x of LHS from both integral and fractional part of fraction gets cancelled.....
$3x + 3 = 4 + 4x \\ \\ 3x - 4x = 4 - 3 \\ \\ - x = 1 \\ x = - 1$