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13 tháng 8 2017
1, \(\dfrac{2ax^2-4ax+2a}{5b-5bx^2}\)
\(=\dfrac{2a\left(x^2-2x+1\right)}{5b\left(1-x^2\right)}\)
\(=\dfrac{2a\left(x-1\right)^2}{5b\left(1-x\right)\left(1+x\right)}\)
\(=\dfrac{2a\left(x-1\right)}{5b\left(x+1\right)}\)
2, \(\dfrac{x^2+4x+3}{2x+6}\)
\(=\dfrac{x^2+3x+x+3}{2\left(x+3\right)}\)
\(=\dfrac{x\left(x+3\right)+\left(x+3\right)}{2\left(x+3\right)}\)
\(=\dfrac{\left(x+1\right)\left(x+3\right)}{2\left(x+3\right)}=\dfrac{x+1}{2}\)
3, \(\dfrac{4x^2-4xy}{5x^3-5x^2y}\)
\(=\dfrac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\dfrac{4}{5x}\)
4, \(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}=\dfrac{\left(x+y-z\right)\left(x+y+z\right)}{x+y+z}=x+y-z\)
5, \(\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^6-y^6\right)}\)
\(=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^3-y^3\right)\left(x^3+y^3\right)}=\dfrac{x^3+y^3}{x\left(x^3-y^3\right)}\)
20 tháng 4 2017
Bài giải:
a) 5x2y4 : 10x2y = 510510x2 – 2. y4 – 1 = 1212y3
b) 3434x3y3 : (- 1212x2y2) = 3434 . (-2) . x3 – 2 . y3 – 2 = -3232xy
c) (-xy)10 : (-xy)5 = (-xy)10 – 5 = (-xy)5 = -x5y5.
17 tháng 10 2017
Bài 45: (SBT/12):
a. (5x4 - 3x3 + x2) : 3x2
= (5x4 : 3x2) + (-3x3 : 3x2) + (x2 : 3x2)
=\(\dfrac{5}{2}\)x2 - x + \(\dfrac{1}{3}\)
b. (5xy2 + 9xy - x2y2) : (-xy)
= [5xy2 : (-xy)] + [9xy : (-xy)] + [(-x2y2) : (-xy)]
= -5y - 9 + xy
c. (x3y3 : \(\dfrac{1}{3}\)x2y3 - x3y2) : \(\dfrac{1}{3}\)x2y2
= (x3y3 : \(\dfrac{1}{3}\)x2y2) + (-\(\dfrac{1}{2}\)x2y3 : \(\dfrac{1}{3}\)x2y2) + (-x3y2 : \(\dfrac{1}{3}\)x2y2)
= 3xy - \(\dfrac{3}{2}\)y - 3x
A
7 tháng 5 2017
a. \(x^2y^3.35xy=5.7x^3y^4\)
\(\Leftrightarrow35x^3y^4=35x^3y^4\Rightarrowđpcm\)
\(b.x^2\left(x+2\right).\left(x+2\right)=x\left(x+2\right)^2.x\)
\(\Leftrightarrow x^2\left(x+2\right)^2=x^2\left(x+2\right)^2\Rightarrowđpcm\)
\(c.\left(3-x\right)\left(9-x^2\right)=\left(3+x\right)\left(x^2-6x+9\right)\)
\(\Leftrightarrow\left(3-x\right)\left(3-x\right)\left(3+x\right)=\left(3+x\right)\left(3-x\right)^2\)
\(\Leftrightarrow\left(3-x\right)^2\left(3+x\right)=\left(3-x\right)^2\left(3+x\right)\)
\(\Rightarrowđpcm\)
\(d.5\left(x^3-4x\right)=\left(10-5x\right)\left(-x^2-2x\right)\)
\(\Leftrightarrow5x^3-20x=5x^3-20x\Rightarrowđpcm\)
23 tháng 9 2018
a) ta có : \(\left(3x^5y^2+4x^3y^3-5x^2y^4\right):2x^2y^2=\dfrac{3x^5y^2}{2x^2y^2}+\dfrac{4x^3y^3}{2x^2y^2}-\dfrac{5x^2y^4}{2x^2y^2}\)
\(=\dfrac{3}{2}x^3+2xy-\dfrac{5}{2}y^2\)
b) ta có : \(\left(\dfrac{3}{5}a^6x^3+\dfrac{3}{7}a^3x^4-\dfrac{9}{10}ax^5\right):\dfrac{3}{5}ax^3\)
\(=\left(\dfrac{3}{5}a^6x^3+\dfrac{3}{7}a^3x^4-\dfrac{9}{10}ax^5\right)\dfrac{5}{3ax^3}\)
\(=\dfrac{3}{5}.\dfrac{5}{3}\dfrac{a^6x^3}{ax^3}+\dfrac{3}{7}.\dfrac{5}{3}\dfrac{a^3x^4}{ax^3}-\dfrac{9}{10}.\dfrac{5}{3}\dfrac{ax^5}{ax^3}\)
\(=a^5+\dfrac{5}{7}a^2x-\dfrac{3}{2}a^2\)
HL
7 tháng 11 2017
1)
a) \(\dfrac{5x}{10}=\dfrac{x}{2}\)
b) \(\dfrac{4xy}{2y}=2x\left(y\ne0\right)\)
c) \(\dfrac{21x^2y^3}{6xy}=\dfrac{7xy^2}{2}\left(xy\ne0\right)\)
d) \(\dfrac{2x+2y}{4}=\dfrac{2\left(x+y\right)}{4}=\dfrac{x+y}{2}\)
e) \(\dfrac{5x-5y}{3x-3y}=\dfrac{5\left(x-y\right)}{3\left(x-y\right)}=\dfrac{5}{3}\left(x\ne y\right)\)
f) \(\dfrac{-15x\left(x-y\right)}{3\left(y-x\right)}=-5x\dfrac{x-y}{y-x}=-5x\dfrac{x-y}{-\left(x-y\right)}\)
\(=-5x.\left(-1\right)=5x\left(x\ne y\right)\)
2)
a) Nhớ ghi ĐK vào nhá, lười quá :V\(\dfrac{x^2-16}{4x-x^2}=-\dfrac{\left(x-4\right)\left(x+4\right)}{x^2-4x}=\dfrac{\left(x-4\right)\left(x+4\right)}{x\left(x-4\right)}=\dfrac{x+4}{x}\)
b) \(\dfrac{x^2+4x+3}{2x+6}=\dfrac{x^2+3x+x+3}{2\left(x+3\right)}=\dfrac{x\left(x+3\right)+\left(x+3\right)}{2\left(x+3\right)}\)
\(=\dfrac{\left(x+3\right)\left(x+1\right)}{2\left(x+3\right)}=\dfrac{x+1}{2}\)
c) \(\dfrac{15x\left(x+3\right)^3}{5y\left(x+y\right)^2}=\dfrac{3x\left(x+3\right)^3}{y\left(x+y\right)^2}\) ( câu này có gì đó sai sai )
d) \(\dfrac{5\left(x-y\right)-3\left(y-x\right)}{10\left(x-y\right)}=\dfrac{5\left(x-y\right)+3\left(x-y\right)}{10\left(x-y\right)}\)
\(=\dfrac{8\left(x-y\right)}{10\left(x-y\right)}=\dfrac{8}{10}=\dfrac{4}{5}\)
e) \(\dfrac{2x+2y+5x+5y}{2x+2y-5x-5y}=\dfrac{2\left(x+y\right)+5\left(x+y\right)}{2\left(x+y\right)-5\left(x+y\right)}\)
\(=\dfrac{7\left(x+y\right)}{-3\left(x+y\right)}=-\dfrac{7}{3}\)
\(\dfrac{3}{5}\cdot x^2y^5\cdot x^3y^2\cdot\dfrac{-2}{3}\)
\(=\dfrac{3}{5}\cdot\dfrac{-2}{3}\cdot x^2\cdot x^3\cdot y^5\cdot y^2\)
\(=-\dfrac{2}{5}x^5y^7\)
\(\dfrac{3}{5}x^2y^5x^3y^2\cdot\dfrac{-2}{3}\\ =\left(\dfrac{3}{5}\cdot\dfrac{-2}{3}\right)\cdot\left(x^2\cdot x^3\right)\cdot\left(y^5\cdot y^2\right)\\ =-\dfrac{2}{5}x^5y^7\)