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a/ \(=\left(\frac{2\left(1-2x\right)-\left(4x^2+1\right)-\left(1+2x\right)}{1-4x^2}\right).\frac{4x^2-1}{2}=\frac{2-4x-4x^2-1-1-2x}{1-4x^2}.\frac{4x^2-1}{2}=\frac{-4-6x-4x^2}{1-4x^2}.\frac{4x^2-1}{2}=\frac{4x^2+6x+4}{2}=2x^2+3x+2\)
b/ có A = 2 \(\Leftrightarrow2x^2+3x+2=2\Rightarrow2x^2+3x=0\Rightarrow x\left(2x+3\right)=0\Rightarrow x=0\)
hoặc \(2x+3=0\Rightarrow2x=-3\Rightarrow x=-\frac{3}{2}\)
Bài 2:
a) ĐK: $x\geq \pm \frac{1}{2}; x\neq 0$
\(\left(\frac{2x+1}{2x-1}-\frac{2x-1}{2x+1}\right):\frac{4x}{10x-5}=\frac{(2x+1)^2-(2x-1)^2}{(2x-1)(2x+1)}.\frac{10x-5}{4x}\)
\(\frac{4x^2+4x+1-(4x^2-4x+1)}{(2x-1)(2x+1)}.\frac{5(2x-1)}{4x}=\frac{8x}{(2x-1)(2x+1)}.\frac{5(2x-1)}{4x}\)
\(=\frac{10}{2x+1}\)
b) ĐK : $x\neq 0;-1$
\(\left(\frac{1}{x^2+x}-\frac{2-x}{x+1}\right):\left(\frac{1}{x}+x-2\right)=\left(\frac{1}{x(x+1)}-\frac{x(2-x)}{x(x+1)}\right):\frac{1+x^2-2x}{x}\)
\(=\frac{1-2x+x^2}{x(x+1)}.\frac{x}{1+x^2-2x}=\frac{x}{x(x+1)}=\frac{1}{x+1}\)
Bài 3:
a) ĐKXĐ: \(x\neq \pm 1\)
b)
\(A=\left(\frac{x+1}{2x-2}-\frac{3}{1-x^2}-\frac{x+3}{2x+2}\right).\frac{4x^2-4}{5}\)
\(=\left[\frac{(x+1)^2}{2(x-1)(x+1)}+\frac{6}{2(x-1)(x+1)}-\frac{(x+3)(x-1)}{2(x+1)(x-1)}\right].\frac{4(x^2-1)}{5}\)
\(=\frac{(x+1)^2+6-(x^2+2x-3)}{2(x-1)(x+1)}.\frac{4(x-1)(x+1)}{5}\)
\(=\frac{10}{2(x-1)(x+1)}.\frac{4(x-1)(x+1)}{5}=4\)
a, ĐKXĐ : x khác -1 và 1
b, A = 2x^2+4x+2/(x-1).(x+1) . (x-1)/10
= 2.(x^2+2x+1)/10.(x+1)
= (x+1)^2/5.(x+1)
= x+1/5
k mk nha
a, ĐKXĐ: \(x\ne\pm1\)
b, \(A=\left(\frac{2x}{x-1}+\frac{4x}{x^2-1}-\frac{2}{x+1}\right)\frac{x-1}{10}\)
\(A=\left(\frac{2x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{4x}{\left(x-1\right)\left(x+1\right)}-\frac{2\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\right)\frac{x-1}{10}\)
\(A=\frac{2x^2+2x+4x-2x+2}{\left(x-1\right)\left(x+1\right)}.\frac{x-1}{10}\)
\(A=\frac{2x^2+4x+2}{10\left(x+1\right)}\)
\(A=\frac{2\left(x+1\right)^2}{10\left(x+1\right)}\)
\(A=\frac{\left(x+1\right)}{5}\)