Toán Rút gọn biểu thức A= 2x-1/2x+1 : ( 2x-1+ 2-4x/2x+1) – 4018/1- 2x ⇒ 03/08/2021 By Josie Rút gọn biểu thức A= 2x-1/2x+1 : ( 2x-1+ 2-4x/2x+1) – 4018/1- 2x ⇒
Đáp án: \(A = \frac{{2011}}{{(x – \frac{1}{2})}}\) Giải thích các bước giải: \(\begin{array}{l}A = \frac{{2x – 1}}{{2x + 1}} \div (2x – 1 + \frac{{2 – 4x}}{{2x + 1}}) – \frac{{4018}}{{1 – 2x}}\\A = \frac{{2x – 1}}{{2x + 1}} \div (\frac{{4{x^2} – 1 + 2 – 4x}}{{2x + 1}}) + \frac{{4018}}{{2x – 1}}\\A = \frac{{2x – 1}}{{4{x^2} – 1 + 2 – 4x}} + \frac{{4018}}{{2x – 1}}\\A = \frac{{2(x – \frac{1}{2})}}{{{{(x – \frac{1}{2})}^2}}} + \frac{{2 \times 2009}}{{2(x – \frac{1}{2})}}\\A = \frac{2}{{(x – \frac{1}{2})}} + \frac{{2009}}{{(x – \frac{1}{2})}}\\A = \frac{{2011}}{{(x – \frac{1}{2})}}\end{array}\) Trả lời
Đáp án:
\(A = \frac{{2011}}{{(x – \frac{1}{2})}}\)
Giải thích các bước giải:
\(\begin{array}{l}
A = \frac{{2x – 1}}{{2x + 1}} \div (2x – 1 + \frac{{2 – 4x}}{{2x + 1}}) – \frac{{4018}}{{1 – 2x}}\\
A = \frac{{2x – 1}}{{2x + 1}} \div (\frac{{4{x^2} – 1 + 2 – 4x}}{{2x + 1}}) + \frac{{4018}}{{2x – 1}}\\
A = \frac{{2x – 1}}{{4{x^2} – 1 + 2 – 4x}} + \frac{{4018}}{{2x – 1}}\\
A = \frac{{2(x – \frac{1}{2})}}{{{{(x – \frac{1}{2})}^2}}} + \frac{{2 \times 2009}}{{2(x – \frac{1}{2})}}\\
A = \frac{2}{{(x – \frac{1}{2})}} + \frac{{2009}}{{(x – \frac{1}{2})}}\\
A = \frac{{2011}}{{(x – \frac{1}{2})}}
\end{array}\)