Thực hiện phép tính: (2 x+1/2x-1-2x-1/2x+1):4x/10x-5

Đáp án:

 \(\dfrac{{5\left( {6x – 1} \right)}}{{4x\left( {2x + 1} \right)}}\)

Giải thích các bước giải:

\(\begin{array}{l}
\left( {\dfrac{{2x}}{{2x – 1}} – \dfrac{{2x – 1}}{{2x + 1}}} \right):\dfrac{{4x}}{{10x – 5}}\\
 = \dfrac{{2x\left( {2x + 1} \right) – \left( {2x – 1} \right)\left( {2x – 1} \right)}}{{\left( {2x – 1} \right)\left( {2x + 1} \right)}}:\dfrac{{4x}}{{5\left( {2x – 1} \right)}}\\
 = \dfrac{{4{x^2} + 2x – 4{x^2} + 4x – 1}}{{\left( {2x – 1} \right)\left( {2x + 1} \right)}}.\dfrac{{5\left( {2x – 1} \right)}}{{4x}}\\
 = \dfrac{{6x – 1}}{{\left( {2x – 1} \right)\left( {2x + 1} \right)}}.\dfrac{{5\left( {2x – 1} \right)}}{{4x}}\\
 = \dfrac{{\left( {6x – 1} \right).5\left( {2x – 1} \right)}}{{\left( {2x – 1} \right)\left( {2x + 1} \right).4x}} = \dfrac{{5\left( {6x – 1} \right)}}{{4x\left( {2x + 1} \right)}}
\end{array}\)