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bài 3:

a) 27-x3/5x+5 : 2x-6/3x+3

b) (4x2-16) : 3x+6/7x-2

c) 3x3+3/x-1 : (x2-x+1)

d) 4x+6y/x-1 : 4x2+12xy+9y2/1-x3

 Nguyễn Hạ Băng
1 tháng 1 2018 lúc 21:39

a)\(\dfrac{27-x^3}{5x+5}:\dfrac{2x-6}{3x+3}\)

\(=\dfrac{\left(3-x\right)\left(9+3x+x^2\right)}{5\left(x+1\right)}:\dfrac{2\left(x-3\right)}{3\left(x+1\right)}\)

\(=\dfrac{\left(3-x\right)\left(9+3x+x^2\right)3\left(x+1\right)}{5\left(x+1\right)2\left(x-3\right)}\)

\(=\dfrac{-\left(x-3\right)\left(9+3x+x^2\right)3\left(x+1\right)}{5\left(x+1\right)2\left(x-3\right)}\)

\(=\dfrac{-\left(9+3x+x^2\right)3}{10}\)

b)\(4x^2-16:\dfrac{3x+6}{7x-2}\)

\(=4\left(x^2-4\right):\dfrac{3\left(x+2\right)}{7x-2}\)

\(=4\left(x-2\right)\left(x+2\right)\cdot\dfrac{7x-2}{3\left(x+2\right)}\)

\(=\dfrac{4\left(x-2\right)\left(x+2\right)\left(7x-2\right)}{3\left(x+2\right)}\)

\(=\dfrac{4\left(x-2\right)\left(7x-2\right)}{3}\)

c)\(\dfrac{3x^3+3}{x-1}:x^2-x+1\)

\(=\dfrac{3\left(x^3+1\right)}{x-1}:x^2-x+1\)

\(=\dfrac{3\left(x+1\right)\left(x^2-x+1\right)}{x-1}\cdot\dfrac{1}{x^2-x+1}\)

\(=\dfrac{3\left(x+1\right)}{x-1}\)

d)\(\dfrac{4x+6y}{x-1}:\dfrac{4x^2+12xy+9y^2}{1-x^3}\)

\(=\dfrac{2\left(2x+3y\right)}{x-1}\cdot\dfrac{\left(1-x\right)\left(1+x+x^2\right)}{\left(2x+3y\right)^2}\)

\(=\dfrac{2\left(2x+3y\right)}{x-1}\cdot\dfrac{-\left(x-1\right)\left(1+x+x^2\right)}{\left(2x+3y\right)^2}\)

\(=\dfrac{-2\left(1+x+x^2\right)}{2x+3y}\)

ngoamthanghoa

Hải Ngân
1 tháng 1 2018 lúc 21:58

a) \(\dfrac{27-x^3}{5x+5}:\dfrac{2x-6}{3x+3}\)

\(=\dfrac{27-x^3}{5x+5}.\dfrac{3x+3}{2x-6}\)

\(=\dfrac{\left(3-x\right)\left(9+3x+x^2\right)}{5\left(x+1\right)}.\dfrac{3\left(x+1\right)}{2\left(x-3\right)}\)

\(=-\dfrac{3\left(x-3\right)\left(x^2+3x+9\right)\left(x+1\right)}{10\left(x+1\right)\left(x-3\right)}\)

\(=-\dfrac{3\left(x^2+3x+9\right)}{10}\)

b) \(4x^2-16:\dfrac{3x+6}{7x-2}\)

\(=4x^2-16.\dfrac{7x-2}{3x+6}\)

\(=\dfrac{4\left(x^2-4\right)\left(7x-2\right)}{3\left(x+2\right)}\)

\(=\dfrac{4\left(x-2\right)\left(x+2\right)\left(7x-2\right)}{3\left(x+2\right)}\)

\(=\dfrac{4\left(x-2\right)\left(7x-2\right)}{3}\)

c) \(\dfrac{3x^3+3}{x-1}:x^2-x+1\)

\(=\dfrac{3x^3+3}{x-1}.\dfrac{1}{x^2-x+1}\)

\(=\dfrac{3\left(x^3+1\right)}{\left(x-1\right)\left(x^2-x+1\right)}\)

\(=\dfrac{3\left(x+1\right)\left(x^2-x+1\right)}{\left(x-1\right)\left(x^2-x+1\right)}\)

\(=\dfrac{3\left(x+1\right)}{x-1}\)

d) \(\dfrac{4x+6y}{x-1}:\dfrac{4x^2+12xy+9y^2}{1-x^3}\)

\(=\dfrac{4x+6y}{x-1}.\dfrac{1-x^3}{4x^2+12xy+9y^2}\)

\(=\dfrac{2\left(2x+3y\right)\left(1-x\right)\left(1+x+x^2\right)}{\left(x-1\right)\left(2x+3y\right)^2}\)

\(=-\dfrac{2\left(2x+3y\right)\left(x-1\right)\left(x^2+x+1\right)}{\left(x-1\right)\left(2x+3y\right)^2}\)

\(=-\dfrac{2\left(x^2+x+1\right)}{2x+3y}\)


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