Đáp án:
\(d)\dfrac{{1 - 3x}}{{2x}} = \dfrac{{ - 6{x^2} + 5x - 1}}{{2x\left( {2x - 1} \right)}}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\dfrac{{11}}{{102{x^4}y}} = \dfrac{{11{y^2}}}{{102{x^4}{y^3}}}\\
\dfrac{3}{{34x{y^3}}} = \dfrac{{3.3.{x^3}}}{{102{x^4}{y^3}}} = \dfrac{{9{x^3}}}{{102{x^4}{y^3}}}\\
c)\dfrac{5}{{2{x^2} - 8}} = \dfrac{5}{{2\left( {x - 2} \right)\left( {x + 2} \right)}} = \dfrac{{5.2}}{{4\left( {x + 2} \right)\left( {x - 2} \right)}}\\
= \dfrac{{10}}{{4\left( {x + 2} \right)\left( {x - 2} \right)}}\\
\dfrac{3}{{4\left( {x + 2} \right)}} = \dfrac{{3\left( {x - 2} \right)}}{{4\left( {x + 2} \right)\left( {x - 2} \right)}} = \dfrac{{3x - 6}}{{4\left( {x + 2} \right)\left( {x - 2} \right)}}\\
b)\dfrac{{3 + 2x}}{{10{x^4}y}} = \dfrac{{\left( {3 + 2x} \right).12{y^4}}}{{120{x^4}{y^5}}} = \dfrac{{36{y^4} + 24x{y^4}}}{{120{x^4}{y^5}}}\\
\dfrac{5}{{8{x^2}{y^2}}} = \dfrac{{5.15.{x^2}{y^3}}}{{120{x^4}{y^5}}} = \dfrac{{75{x^2}{y^3}}}{{120{x^4}{y^5}}}\\
\dfrac{2}{{3x{y^5}}} = \dfrac{{2.40.{x^3}}}{{120{x^4}{y^5}}} = \dfrac{{80{x^3}}}{{120{x^4}{y^5}}}\\
d)\dfrac{{1 - 3x}}{{2x}} = \dfrac{{\left( {1 - 3x} \right)\left( {2x - 1} \right)}}{{2x\left( {2x - 1} \right)}} = \dfrac{{ - 6{x^2} + 5x - 1}}{{2x\left( {2x - 1} \right)}}\\
\dfrac{{3x - 2}}{{2x - 1}} = \dfrac{{2x\left( {3x - 2} \right)}}{{2x\left( {2x - 1} \right)}} = \dfrac{{6{x^2} - 4x}}{{2x\left( {2x - 1} \right)}}\\
\dfrac{{3x - 2}}{{2x\left( {2x - 1} \right)}}
\end{array}\)
