Bepaal die waarde van x: \( \frac{1}{{{x^2} - 1}} + \frac{2}{{x - 1}} = \frac{1}{x} \)
\( \( \begin{align} \frac{1}{{{x^2} - 1}} + \frac{2}{{x - 1}} &= \frac{1}{x}\\ \frac{1}{{\left( {x - 1} \right)\left( {x + 1} \right)}} + \frac{2}{{\left( {x - 1} \right)}} &= \frac{1}{x}\\ KGV &= x\left( {x - 1} \right)\left( {x + 1} \right)\\ 1\left( x \right) + 2x\left( {x + 1} \right) &= 1\left( {x - 1} \right)\left( {x + 1} \right)\\ x + 2{x^2} + 2x &= {x^2} - 1\\ x + 2{x^2} + 2x - {x^2} + 1 &= 0\\ {x^2} + 3x + 1 &= 0\\ x &= \frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\\ x &= \frac{{ - \left( 3 \right) \pm \sqrt {{{\left( 3 \right)}^2} - 4\left( 1 \right)\left( 1 \right)} }}{{2\left( 1 \right)}}\\ x &= \frac{{ - 3 \pm \sqrt 5 }}{2}\\ x &= - 0.4\,\,\,of\,\,\,x = - 2.6 \end{align} \) \)
Beperkings:
\( {x \ne 0} \)
\( \begin{align} x - 1 &\ne 0\\ x &\ne 1 \end{align} \)
\( \begin{align} x + 1 &\ne 0\\ x &\ne - 1 \end{align} \)