Thực hiện phép tính:
(2x3-21x2+67x-60):(x-5)
(x^4+2x^3+x-25):(x^2+5)
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a) \(\left(2x-y\right)\left(4x^2-2xy+y^2\right)\)
\(=8x^3-4x^2y+2xy^2-4xy^2+2xy^2-y^3\)
\(=8x^3-8x^2y+4xy^2-y^3\)
b) \(\left(6x^5y^2-9x^4y^3+15x^3y^4\right):3x^3y^2\)
\(=2x^2-3xy+5y^2\)
f: \(=\dfrac{2x^3-10x^2-11x^2+55x+12x-60}{x-5}=2x^2-11x+12\)
Bài 1:
a: \(=2x^2-3xy+5y^2\)
b: \(=\dfrac{2x^3-10x^2-11x^2+55x+12x-60}{x-5}=2x^2-11x+12\)
c: \(=\dfrac{6x^3+3x^2-10x^2-5x+4x+2}{2x+1}=3x^2-5x+2\)
c: \(=\dfrac{\left(x+3\right)^2-y^2}{x+y+3}=x+3-y\)
\(a,=10x^3-5x^2+5x\\ b,=x^3+27\\ c,=\dfrac{5}{2}xy-1-\dfrac{1}{2}y\\ d,=\left(2x^3-10x^2-11x^2+55x+12x-60\right):\left(x-5\right)\\ =\left[2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\right]:\left(x-5\right)\\ =2x^2-11x+12\)
1: ĐKXĐ: \(x\notin\left\{0;3\right\}\)
\(\dfrac{x+3}{x}-\dfrac{x}{x-3}+\dfrac{9}{x^2-3x}\)
\(=\dfrac{x+3}{x}-\dfrac{x}{x-3}+\dfrac{9}{x\left(x-3\right)}\)
\(=\dfrac{\left(x+3\right)\left(x-3\right)-x^2+9}{x\left(x-3\right)}\)
\(=\dfrac{x^2-9-x^2+9}{x\left(x-3\right)}\)
=0
2: ĐKXĐ: \(x\notin\left\{0;1\right\}\)
\(\dfrac{3}{x}-\dfrac{5}{x-1}+\dfrac{3x+2}{x^2-x}\)
\(=\dfrac{3}{x}-\dfrac{5}{x-1}+\dfrac{3x+2}{x\left(x-1\right)}\)
\(=\dfrac{3x-3-5x+3x+2}{x\left(x-1\right)}\)
\(=\dfrac{x-1}{x\left(x-1\right)}=\dfrac{1}{x}\)