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ta có : \(\left(a-\dfrac{x^2+a^2}{x+a}\right).\left(\dfrac{2a}{x}-\dfrac{4a}{x-a}\right)\)
\(=\dfrac{-x^2-a^2+ax+a^2}{x+a}.\dfrac{2a\left(x-a\right)-4ax}{x\left(x-a\right)}\)
\(=\dfrac{-x^2+ax}{x+a}.\dfrac{2ax-2a^2-4ax}{x\left(x-a\right)}\)
\(=\dfrac{-x\left(x-a\right)}{x+a}.\dfrac{-2a^2-2ax}{x\left(x-a\right)}\)
\(=\dfrac{-x\left(x-a\right)}{x+a}.\dfrac{-2a\left(a+x\right)}{x\left(x-a\right)}=\dfrac{2a}{1}=2a\) vì a nguyên \(\Rightarrow2a\) nguyên (đpcm)
1: \(\Leftrightarrow\left(x+2\right)\left(x-2\right)+3\left(x+1\right)=3+x^2-x-2\)
\(\Leftrightarrow x^2-x+1=x^2-4+3x+3=x^2+3x-1\)
=>-4x=-2
hay x=1/2
2: \(\Leftrightarrow\left(x+6\right)^2+\left(x-5\right)^2=2x^2+23x+61\)
\(\Leftrightarrow x^2+12x+36+x^2-10x+25=2x^2+23x+61\)
\(\Leftrightarrow2x^2+23x+61=2x^2+2x+11\)
=>21x=-50
hay x=-50/21
3: \(\Leftrightarrow6\left(x-8\right)+\left(x+2\right)\left(x-5\right)=-18-\left(x-5\right)\left(x-8\right)\)
\(\Leftrightarrow6x-48+x^2-3x-10+18+x^2-13x+40=0\)
\(\Leftrightarrow2x^2-10x=0\)
=>2x(x-5)=0
=>x=0(nhận) hoặc x=5(loại)
Lời giải của bạn Nhật Linh đúng rồi, tuy nhiên cần thêm điều kiện để A có nghĩa: \(x\ne\pm2\)
1,
\(x^2-2ax+a^2=\left(x-a\right)^2\)
\(x^2-ax=x\left(x-a\right)\)
Vậy MSC: \(\left(x-a\right)^2x\)
2,
\(x^3-1=\left(x-1\right)\left(x^2+x+1\right)\)
\(x^2-x=x\left(x-1\right)\)
\(x^2+x+1\)
vậy MSC là: \(x\left(x-1\right)\left(x^2+x+1\right)\)
a)
\(A=\dfrac{1+x^2+\dfrac{1}{x}}{2+\dfrac{1}{x}}=1\Leftrightarrow\left\{{}\begin{matrix}x\ne0;x\ne-\dfrac{1}{2}\\1+x^2+\dfrac{1}{x}=2+\dfrac{1}{x}\end{matrix}\right.\)
\(\Rightarrow x^2=1\Rightarrow x=\pm1\)
a: \(=\dfrac{4a^2-4a+1-4a^2-2a+6a+3}{\left(2a-1\right)\left(2a+1\right)}\)
\(=\dfrac{4}{\left(2a-1\right)\left(2a+1\right)}\)
b: \(=\dfrac{x-1-x-1+2x^2}{\left(x-1\right)\left(x+1\right)}=2\)
d: \(=\dfrac{x-5+6x}{x\left(x+3\right)}=\dfrac{7x-5}{x\left(x+3\right)}\)
e: \(=\dfrac{x^2-4+3}{x-2}=\dfrac{x^2-1}{x-2}\)
i: \(=\dfrac{x}{x\left(x-4\right)}-\dfrac{3}{5x}=\dfrac{1}{x-4}-\dfrac{3}{5x}\)
\(=\dfrac{5x-3x+12}{5x\left(x-4\right)}=\dfrac{2x+12}{5x\left(x-4\right)}\)
Hả chỉ cho bài này r mak
tao đăng lên hồi nào rồi mà ba đâu phải mới đăng đâu
\(A=a+\dfrac{\left(2a+x\right)\left(2+x\right)-\left(2a-x\right)\left(2-x\right)-4a}{\left(2-x\right)\left(2+x\right)}\)
\(=a+\dfrac{4a+2ax+2x+x^2-4a+2ax+2x-x^2-4a}{\left(2-x\right)\left(2+x\right)}\)
\(=a+\dfrac{4ax+4x-4a}{\left(2-x\right)\left(2+x\right)}\)
\(=\dfrac{a\left(4-x^2\right)+4ax+4x-4a}{4-x^2}\)
\(=\dfrac{4a-ax^2+4ax+4x-4a}{4-x^2}\)
\(=\dfrac{-ax^2+4ax+4x}{4-x^2}\)
\(=\dfrac{x\left(-ax+4a+4\right)}{4-x^2}\)
\(=\left[\dfrac{a}{a+1}\cdot\left(-a\cdot\dfrac{a}{a+1}+4a+4\right)\right]:\left[4-\dfrac{a^2}{\left(a+1\right)^2}\right]\)
\(=\left(\dfrac{a}{a+1}\cdot\left(\dfrac{-a^2+4a^2+8a+4}{a+1}\right)\right):\left[\dfrac{4\left(a+1\right)^2-a^2}{\left(a+1\right)^2}\right]\)
\(=\dfrac{a\left(3a^2+8a+4\right)}{4\left(a+1\right)^2-a^2}=\dfrac{a\left(3a^2+6a+2a+4\right)}{\left(2a+2\right)^2-a^2}\)
\(=\dfrac{a\left(a+2\right)\left(3a+2\right)}{\left(a+2\right)\left(3a+2\right)}=a\)