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a: \(A=\dfrac{3x^2-4+2\left(x+1\right)-2\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}\cdot\dfrac{x+1}{x+1-x}\)
\(=\dfrac{3x^2-4+2x+2-2x+2}{\left(x+1\right)\left(x-1\right)}\cdot\dfrac{x+1}{1}\)
\(=\dfrac{3x^2}{\left(x+1\right)\left(x-1\right)}\cdot\dfrac{x+1}{1}=\dfrac{3x^2}{x-1}\)
b: Để A chia hết cho 2013 thì A=2013k
=>3x2=2013k(x-1)(k∈Z)
Bài 1:
a) Ta có: \(P=1+\dfrac{3}{x^2+5x+6}:\left(\dfrac{8x^2}{4x^3-8x^2}-\dfrac{3x}{3x^2-12}-\dfrac{1}{x+2}\right)\)
\(=1+\dfrac{3}{\left(x+2\right)\left(x+3\right)}:\left(\dfrac{8x^2}{4x^2\left(x-2\right)}-\dfrac{3x}{3\left(x-2\right)\left(x+2\right)}-\dfrac{1}{x+2}\right)\)
\(=1+\dfrac{3}{\left(x+2\right)\left(x+3\right)}:\left(\dfrac{4}{x-2}-\dfrac{x}{\left(x-2\right)\left(x+2\right)}-\dfrac{1}{x+2}\right)\)
\(=1+\dfrac{3}{\left(x+2\right)\left(x+3\right)}:\dfrac{4\left(x+2\right)-x-\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=1+\dfrac{3}{\left(x+2\right)\left(x+3\right)}\cdot\dfrac{\left(x-2\right)\left(x+2\right)}{4x+8-x-x+2}\)
\(=1+3\cdot\dfrac{\left(x-2\right)}{\left(x+3\right)\left(2x+10\right)}\)
\(=1+\dfrac{3\left(x-2\right)}{\left(x+3\right)\left(2x+10\right)}\)
\(=\dfrac{\left(x+3\right)\left(2x+10\right)+3\left(x-2\right)}{\left(x+3\right)\left(2x+10\right)}\)
\(=\dfrac{2x^2+10x+6x+30+3x-6}{\left(x+3\right)\left(2x+10\right)}\)
\(=\dfrac{2x^2+19x-6}{\left(x+3\right)\left(2x+10\right)}\)
a: \(A=\dfrac{2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\sqrt{x}-1}{\sqrt{x}}=\dfrac{2\sqrt{x}+1}{x+\sqrt{x}}\)
a) \(ĐKXĐ:\) \(x\ne\pm1\)
\(A=\left(\frac{3x^2-4}{x^2-1}-\frac{2}{1-x}-\frac{2}{x+1}\right):\left(\frac{1-x}{x+1}\right)\)
\(=\left(\frac{3x^2-4}{\left(x-1\right)\left(x+1\right)}+\frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\frac{2\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\right).\frac{x+1}{1-x}\)
\(=\frac{3x^2-4+2x+2-2x+2}{\left(x-1\right)\left(x+1\right)}.\frac{x+1}{1-x}\)
\(=\frac{3x^2}{\left(x-1\right)\left(x+1\right)}.\frac{x+1}{1-x}\)
\(=-\frac{3x^2}{\left(x-1\right)^2}\)