cho biểu thức A=(1/2x-1+3/1-4x^2-2/2x+1):x^2/2x^2+x a) rút gọn A b)Tính GTBT tại x=2 c)tìm x để gía trị của A=4 d)tìm x để A=1

Đáp án:

$\begin{array}{l}
a)Dkxd:\left\{ \begin{array}{l}
2x - 1 \ne 0\\
1 - 4{x^2} \ne 0\\
2x + 1 \ne 0\\
x \ne 0
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x \ne 0\\
x \ne  - \frac{1}{2}\\
x \ne \frac{1}{2}
\end{array} \right.\\
A = \left( {\frac{1}{{2x - 1}} + \frac{3}{{1 - 4{x^2}}} - \frac{2}{{2x + 1}}} \right):\frac{{{x^2}}}{{2{x^2} + x}}\\
 = \frac{{2x + 1 - 3 - 2\left( {2x - 1} \right)}}{{\left( {2x - 1} \right)\left( {2x + 1} \right)}}.\frac{{x\left( {2x + 1} \right)}}{{{x^2}}}\\
 = \frac{{2x - 2 - 4x + 2}}{{2x - 1}}.\frac{1}{x}\\
 = \frac{{ - 2x}}{{x\left( {2x - 1} \right)}}\\
 = \frac{{ - 2}}{{2x - 1}}\\
 = \frac{2}{{1 - 2x}}\\
b)x = 2\left( {tmdk} \right)\\
 \Rightarrow A = \frac{2}{{1 - 2.2}} = \frac{{ - 2}}{3}\\
c)A = 4\\
 \Rightarrow \frac{2}{{1 - 2x}} = 4\\
 \Rightarrow 1 - 2x = \frac{1}{2}\\
 \Rightarrow x = \frac{1}{4}\left( {tmdk} \right)\\
d)A = 1\\
 \Rightarrow \frac{2}{{1 - 2x}} = 1\\
 \Rightarrow 1 - 2x = 2\\
 \Rightarrow x =  - \frac{1}{2}\left( {ktm} \right)\\
Vậy\,ko\,có\,x\,để\,A = 1
\end{array}$