Thực hiện các phép tính:a) (frac{{x - 12}}{{6{ m{x}} - 36}} + frac{6}{{{x^2} - 6x}})              &nb

* Hướng dẫn giải

\(a){\rm{  }}\frac{{x - 12}}{{6{\rm{x}} - 36}} + \frac{6}{{{x^2} - 6x}}\)

Giải

\(\begin{array}{l}
6{\rm{x}} - 36 = 6\left( {x - 6} \right);{x^2} - 6x = x\left( {x - 6} \right)\\
MTC:6x\left( {x - 6} \right)\\
{\rm{   }}\frac{{x - 12}}{{6{\rm{x}} - 36}} + \frac{6}{{{x^2} - 6x}} = \frac{{x - 12}}{{6\left( {x - 6} \right)}} + \frac{6}{{x\left( {x - 6} \right)}} = \frac{{\left( {x - 12} \right).x}}{{6\left( {x - 6} \right).x}} + \frac{{6.6}}{{x\left( {x - 6} \right).6}}\\
 = \frac{{{x^2} - 12x + 36}}{{6x\left( {x - 6} \right)}} = \frac{{{{\left( {x - 6} \right)}^2}}}{{6x\left( {x - 6} \right)}} = \frac{{\left( {x - 6} \right)}}{{6x}}
\end{array}\)

\(\begin{array}{l}
{\rm{b)  }}\frac{1}{x} - \frac{1}{{x + 1}}\\
MTC:x\left( {x + 1} \right)\\
{\rm{   }}\frac{1}{x} - \frac{1}{{x + 1}} = \frac{{1.\left( {x + 1} \right)}}{{x.\left( {x + 1} \right)}} - \frac{{1.x}}{{\left( {x + 1} \right).x}} = \frac{{x + 1 - x}}{{x\left( {x + 1} \right)}} = \frac{1}{{x\left( {x + 1} \right)}}
\end{array}\)