Question
Solve equation using factorisation method:
$\frac{6}{x}=1+x$
$\frac{6}{x}=1+x$
✓
Answer
$\frac{6}{x}=1+x$
$\Rightarrow 6 = x + x^2$
$\Rightarrow x^2 + x - 6 = 0$
$\Rightarrow x2 + 3x - 2x - 6 = 0$
$\Rightarrow x(x +3) -2 (x + 3) = 0$
$\Rightarrow (x + 3) (x -2) = 0$
Since $x + 3 = 0$ or $x -2 = 0$
then $x = -3$ or $x = 2$
$\Rightarrow 6 = x + x^2$
$\Rightarrow x^2 + x - 6 = 0$
$\Rightarrow x2 + 3x - 2x - 6 = 0$
$\Rightarrow x(x +3) -2 (x + 3) = 0$
$\Rightarrow (x + 3) (x -2) = 0$
Since $x + 3 = 0$ or $x -2 = 0$
then $x = -3$ or $x = 2$
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