Đáp án:
5) \(\dfrac{{x + 6}}{x}\)
Giải thích các bước giải:
\(\begin{array}{l}
1)DK:x \ne y \ne 0\\
\dfrac{{4x - 1 - 7x + 1}}{{3{x^2}y}} = \dfrac{{ - 3x}}{{3{x^2}y}} - \dfrac{1}{{xy}}\\
3)DK:x \ne \dfrac{2}{5}\\
\dfrac{{20x - 7 + 3x + 5}}{{10x - 4}} = \dfrac{{23x - 2}}{{10x - 4}}\\
5)DK:x \ne \left\{ { - 6;0} \right\}\\
\dfrac{{12\left( {x + 6} \right) + {x^2} - 36}}{{x\left( {x + 6} \right)}} = \dfrac{{12\left( {x + 6} \right) + \left( {x - 6} \right)\left( {x + 6} \right)}}{{x\left( {x + 6} \right)}}\\
= \dfrac{{\left( {x + 6} \right)\left( {12 + x - 6} \right)}}{{x\left( {x + 6} \right)}} = \dfrac{{x + 6}}{x}\\
7)DK:x \ne \pm \dfrac{1}{3}\\
\dfrac{{3x - 1}}{{3x + 1}} - \dfrac{{3x - 1}}{{3x + 1}} - \dfrac{4}{{\left( {3x - 1} \right)\left( {3x + 1} \right)}} = - \dfrac{4}{{\left( {3x - 1} \right)\left( {3x + 1} \right)}}\\
9)DK:x \ne \pm y\\
\dfrac{{{{\left( {x + y} \right)}^2} - {{\left( {x - y} \right)}^2} + 2.2{y^2}}}{{2\left( {x + y} \right)\left( {x - y} \right)}}\\
= \dfrac{{{x^2} + 2xy + {y^2} - {x^2} + 2xy - {y^2} + 4{y^2}}}{{2\left( {x + y} \right)\left( {x - y} \right)}}\\
= \dfrac{{4{y^2} + 4xy}}{{2\left( {x + y} \right)\left( {x - y} \right)}}\\
= \dfrac{{4y\left( {x + y} \right)}}{{2\left( {x + y} \right)\left( {x - y} \right)}} = \dfrac{{2y}}{{x - y}}
\end{array}\)
