Bài 6. Rút gọn các phân thức sau
c) \(\frac{2ax^2-4ax+2a}{5b-5b^2}\)
f) \(\frac{x^6+2x^3y^3+y^6}{x^7-xy^6}\)
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30 tháng 1
\(\dfrac{2a\cdot x^2-4ax+2a}{5b-5bx^2}\)
\(=\dfrac{2a\left(x^2-2x+1\right)}{5b\left(1-x^2\right)}\)
\(=\dfrac{-2a\left(x-1\right)^2}{5b\left(x-1\right)\left(x+1\right)}=\dfrac{-2a\left(x-1\right)}{5b\left(x+1\right)}\)
\(\dfrac{4x^2-4xy}{5x^3-5x^2y}\)
\(=\dfrac{4x\cdot x-4x\cdot y}{5x^2\cdot x-5x^2\cdot y}\)
\(=\dfrac{4x\left(x-y\right)}{5x^2\left(x-y\right)}=\dfrac{4}{5x}\)
\(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}\)
\(=\dfrac{\left(x+y+z\right)\left(x+y-z\right)}{x+y+z}\)
=x+y-z
\(\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}\)
\(=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^6-y^6\right)}\)
\(=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^3+y^3\right)\left(x^3-y^3\right)}=\dfrac{x^3+y^3}{x\left(x^3-y^3\right)}\)
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, \(\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^6-y^6\right)}\)
\(=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^3-y^3\right)\left(x^3+y^3\right)}=\dfrac{x^3+y^3}{x\left(x^3-y^3\right)}\)
HB
1
17 tháng 2 2023
\(A=\dfrac{2a\left(x^2-2x+1\right)}{5b\left(1-b\right)}=\dfrac{2a\left(x-1\right)^2}{5b\left(1-b\right)}\)
\(B=\dfrac{\left(x+y+z\right)\left(x+y-z\right)}{x+y+z}=x+y-z\)
6 tháng 12 2016
B=\(\frac{5\left(x-y\right)-3\left(x-y\right)}{10\left(x-y\right)}\)
B=\(\frac{\left(x-y\right)\left(5-3\right)}{10\left(x-y\right)}\)
B= \(\frac{\left(x-y\right)2}{10\left(x-y\right)}\)
B= 5
vậy B=5
RB
1
11 tháng 5 2022
\(a,\dfrac{2ax^2-4ax+2a}{5b-5bx^2}\)
\(=\dfrac{2a\left(x^2-2x+1\right)}{5b\left(1-x^2\right)}\)
\(=\dfrac{2a\left(x-1^2\right)}{5b\left(x-1\right)\left(1+x\right)}\)
\(=\dfrac{2a\left(x-1\right)}{5b\left(x+1\right)}\)
\(b,\dfrac{\left(x+y\right)^2-z^2}{x+y+z}\)
\(=\dfrac{\left(x+y-z\right)\left(x+y+z\right)}{x+y+z}=x+y-z\)
NN
1
29 tháng 10 2020
\(\frac{2ax^2-4ax+2a}{5b-5bx^2}\)
\(=-\frac{2a\left(x-1\right)^2}{5b\left(x+1\right)\left(x-1\right)}\)
\(=-\frac{2a\left(x-1\right)}{5b\left(x+1\right)}\)
CN
1
22 tháng 2 2020
tôi cũng cung thiên yết nè nhưng lại là cậu bé mà thiên yết hợp với cung gì nhất vậy add friend nha
TX
2
7 tháng 2 2021
Ta có: \(\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}\)
\(=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^6-y^6\right)}\)
\(=\dfrac{\left(x^3+y^3\right)\left(x^3+y^3\right)}{x\left(x^3+y^3\right)\left(x^3-y^3\right)}\)
\(=\dfrac{x^3+y^3}{x\left(x^3-y^3\right)}\)
\(=\dfrac{\left(x+y\right)\left(x^2-xy+y^2\right)}{x\left(x-y\right)\left(x^2+xy+y^2\right)}\)
7 tháng 2 2021
\(\dfrac{x^6+2x^3y^3+y^6}{x^7-xy^6}=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^6-y^6\right)}=\dfrac{\left(x^3+y^3\right)^2}{x\left(x^3-y^3\right)\left(x^3+y^3\right)}=\dfrac{x^3+y^3}{x\left(x^3-y^3\right)}=\dfrac{\left(x+y\right)\left(x^2-xy+y^2\right)}{\left(x^2-y^2\right)\left(x^2+y^2\right)}=\dfrac{\left(x+y\right)\left(x^2-xy+y^2\right)}{\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)}=\dfrac{x^2-xy+y^2}{x^3+xy^2-x^2y-y^3}\)