đk : x >= 0 ; x khác 4 

\(A=\dfrac{2\sqrt{x}-4-\sqrt{x}-2+4}{x-4}=\dfrac{\sqrt{x}-2}{x-4}=\dfrac{1}{\sqrt{x}+2}\)

\(A=\dfrac{2}{\sqrt{x}+2}-\dfrac{1}{\sqrt{x}-2}+\dfrac{4}{x-4}\left(đk:x>2\right)\)

\(=\dfrac{2\left(\sqrt{x}-2\right)-\left(\sqrt{x}+2\right)+4}{x-4}\)

\(=\dfrac{2\sqrt{x}-4-\sqrt{x}-2+4}{x-4}=\dfrac{\sqrt{x}-2}{x-4}=\dfrac{1}{\sqrt{x}+2}\)

ĐKXĐ: x khác 4; x ≥ 0

\(A=\dfrac{2\sqrt{x}-4-\sqrt{x}-2+4}{x-4}=\dfrac{\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{1}{\sqrt{x}+2}\)

a) A = 2x^2 + 2y^2

a, \(A=\left(x-y\right)^2+\left(x+y\right)^2\)

\(=x^2-2xy+y^2+x^2+2xy+y^2\)

\(=2x^2+2y^2\)

a) \(A=\left(x-y\right)^2+\left(x+y\right)^2\\ =x^2-2xy+y^2+x^2+2xy+y^2=2x^2+2y^2\)

b) \(B=\left(2x-1\right)^2-2\left(2x-3\right)^2+4\\ =4x^2-4x+1-2\left(4x^2-12x+9\right)+4\\ =4x^2-4x+1-8x^2+24x-18+4\)

    \(=-4x^2+20x-13\)

\(A=\dfrac{x+2+x-1-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)

\(=\dfrac{\sqrt{x}}{x+\sqrt{x}+1}\)

\(A=\dfrac{15-\sqrt{x}+2\sqrt{x}-10}{x-25}\cdot\dfrac{\sqrt{x}-5}{\sqrt{x}+1}\)

\(=\dfrac{\sqrt{x}+5}{\sqrt{x}+5}\cdot\dfrac{1}{\sqrt{x}+1}=\dfrac{1}{\sqrt{x}+1}\)

\(ĐKXĐ:\hept{\begin{cases}x\ne\pm1\\x\ne-\frac{1}{2}\end{cases}}\)

a) \(A=\left(\frac{1}{x-1}+\frac{x}{x^3-1}\cdot\frac{x^2+x+1}{x+1}\right):\frac{2x+1}{x^2+2x+1}\)

\(\Leftrightarrow A=\left(\frac{1}{x-1}+\frac{x}{\left(x-1\right)\left(x+1\right)}\right):\frac{2x+1}{\left(x+1\right)^2}\)

\(\Leftrightarrow A=\frac{x+1+x}{\left(x-1\right)\left(x+1\right)}\cdot\frac{\left(x+1\right)^2}{2x+1}\)

\(\Leftrightarrow A=\frac{\left(2x+1\right)\left(x+1\right)}{\left(x-1\right)\left(2x+1\right)}\)

\(\Leftrightarrow A=\frac{x+1}{x-1}\)

b) Thay \(x=\frac{1}{2}\)vào A, ta được :

\(A=\frac{\frac{1}{2}+1}{\frac{1}{2}-1}=\frac{\frac{3}{2}}{-\frac{1}{2}}=-3\)

a: Ta có: \(\left(x-2\right)^2-\left(2x-1\right)^2+\left(3x-1\right)\left(x-5\right)\)

\(=x^2-4x+4-4x^2+4x-1+3x^2-15x-x+5\)

\(=-16x+8\)

b: Ta có: \(\left(x-3\right)^3-\left(x+3\right)\left(x^2-3x+9\right)+\left(3x-1\right)\left(3x+1\right)\)

\(=x^3-9x^2+27x-27-x^3-27+9x^2-1\)

=27x-55

\(A=\left(\dfrac{1}{x^2-4x}+\dfrac{2}{16-x^2}+\dfrac{4}{4x+16}\right):\dfrac{1}{4x}\left(x\ne4;x\ne-4;x\ne0\right).\)

\(A=\left(\dfrac{1}{x\left(x-4\right)}+\dfrac{-2}{\left(x+4\right)\left(x-4\right)}+\dfrac{1}{x+4}\right).4x\).

\(A=\dfrac{x+4-2x+x^2-4x}{x\left(x-4\right)\left(x+4\right)}.4x.\)

\(A=\dfrac{x^2-5x+4}{\left(x-4\right)\left(x+4\right)}.4.\)

\(A=\dfrac{\left(x-4\right)\left(x-1\right)}{\left(x-4\right)\left(x+4\right)}.4.\)

\(A=\dfrac{4\left(x-1\right)}{x+4}.\)

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