# How do you multiply (x-2)/ 3=1/ x?

May 9, 2015

Cross multiplication is used here:

$\left(x - 2\right) \times x = 1 \times 3$

we obtain equation:
${x}^{2} - 2 x = 3$
${x}^{2} - 2 x - 3 = 0$

solving this equation by grouping / splitting the middle term:
${x}^{2} - 2 x - 3 = 0$

The middle term $- 2 x = - 3 x + 1 x$ and
The product $- 3 = - 3 \times 1$.

${x}^{2} - 3 x + 1 x - 3 = 0$
grouping by taking out common terms:
$x \left(x - 3\right) + 1 \left(x - 3\right) = 0$
$\left(x - 3\right) + \left(x + 1\right) = 0$

solutions for the equation:
$x = 3 \mathmr{and} x = - 1$