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\(a,=-15x^3+10x^4+20x^2\\ b,=2x^3+2x^2+4x-x^2-x-2=2x^3+x^2+3x-2\)
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\(\left(\dfrac{1}{x}+x-2\right):\left(\dfrac{1}{x^2-x}+1-\dfrac{3}{x-1}\right)\)
\(=\dfrac{x^2-2x+1}{x}:\dfrac{1+x^2-x-3x}{x\left(x-1\right)}\)
\(=\dfrac{\left(x-1\right)^2}{x}\cdot\dfrac{x\left(x-1\right)}{x^2-4x+1}=\dfrac{\left(x-1\right)^3}{x^2-4x+1}\)
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a. \(\left(2x+1\right)^2-4x\left(x-1\right)=4x^2+4x+1-4x^2+4x=8x+1\)
b. \(\left(x-2\right)\left(x+2\right)-\left(x-1\right)^2=x^2-4-x^2+2x-1=2x-5\)
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a, \(\left(x^2-9\right)^2-\left(x-3\right)\left(x+3\right)\left(x^2+9\right)=\left(x^2-9\right)^2-\left(x^2-9\right)\left(x^2+9\right)\)
\(=x^4-18x^2+81-x^4+81=-18x^2+162\)
b, \(\left(x^2+x-3\right)\left(x^2-x+3\right)=\left[x^4-\left(x-3\right)^2\right]\)
\(=x^4-x^2+6x-9\)
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a) = x^2 - 9 - (x^2 + 3x - 10)
= -3x + 1
b) = 3x + 1 - 3x + 19
= 20
a: \(\left(x+3\right)\left(x-3\right)-\left(x-2\right)\left(x+5\right)\)
\(=x^2-9-x^2-3x+10\)
\(=-3x+1\)
b: \(\dfrac{27x^3+1}{9x^2-3x+1}-\left(3x-19\right)\)
\(=3x+1-3x+19\)
=20
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a: \(=\dfrac{x^2-5x+x+4}{x\left(x-2\right)}=\dfrac{x^2-4x+4}{x\left(x-2\right)}=\dfrac{x-2}{x}\)
b: \(=\dfrac{x^2-6x+9+4x^2+8x-4x^2-8x}{\left(x-3\right)\left(x+2\right)}\)
\(=\dfrac{x-3}{x+2}\)
a) \(=\dfrac{x\left(x-5\right)+x+4}{x\left(x-2\right)}=\dfrac{x^2-4x+4}{x\left(x-2\right)}=\dfrac{\left(x-2\right)^2}{x\left(x-2\right)}=\dfrac{x-2}{x}\)
b) \(=\dfrac{\left(x-3\right)^2+4x\left(x+2\right)-8x-4x^2}{\left(x+2\right)\left(x-3\right)}=\dfrac{x^2-6x+9+4x^2+8x-8x-4x^2}{\left(x+2\right)\left(x-3\right)}\)
\(=\dfrac{x^2-6x+9}{\left(x+2\right)\left(x-3\right)}=\dfrac{\left(x-3\right)^2}{\left(x+2\right)\left(x-3\right)}=\dfrac{x-3}{x+2}\)
a) (x-1)(x+1)(x+2)
=\(\left(x^2-1\right)\) (x+2)
= \(x^3+2x^2-x-2\)
TL:
a) (x-1) (x+2)
\(=\left(x^2-1\right)\)(x+2)
\(=x^3\)\(+2x^2\)\(-x-2\)