Rút gọn:
A= -(x+2)(x-5)+(x-1)(x-2)
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Khách
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21 tháng 8 2021
a) \(A=\left(5-x\right)\left(5+x\right)-x\left(4-x\right)-25\\ =25-x^2-4x+x^2-25\\ =-4x\)
b) \(B=\left(x^2+1\right)\left(x+1\right)-\left(x+1\right)^3\\ =x^3+x+x^2+1-x^3-3x^2-3x-1\\ =-2x^2-2x\)
c) \(\left(x+y-2\right)^2-2\left(x+y-2\right)\left(y+x\right)+\left(x+y\right)^2\)
\(=x^2+y^2+4+2xy-4y-4x-2\left(xy+y^2-2y+x^2+xy-2x\right)+x^2+2xy+y^2\)
\(=x^2+y^2+4+2xy-4y-4x-2\left(2xy+y^2-2y+x^2-2x\right)+x^2+2xy+y^2\)
\(=x^2+y^2+4+2xy-4y-4x-4xy-2y^2+4y-2x^2+4x+x^2+2xy+y^2\)
\(=4\)
21 tháng 8 2021
a) \(A=\left(5-x\right)\left(5+x\right)-x\left(4-x\right)-25=25-x^2-4x+x^2-25=-4x\)b) \(B=\left(x^2+1\right)\left(x+1\right)-\left(x+1\right)^3=\left(x+1\right)\left[x^2+1-\left(x+1\right)^2\right]=\left(x+1\right)\left(x^2+1-x^2-2x-1\right)=\left(x+1\right)\left(-2x\right)\)c) \(C=\left(x+y-2\right)^2-2\left(x+y-2\right)\left(y+x\right)+\left(x+y\right)^2=\left(x+y-1-x-y\right)^2=\left(-1\right)^2=1\)
JP
3
LD
11 tháng 1 2022
\(A=\dfrac{x}{x-2}-\dfrac{x^2+x-2}{x^2-4}=\dfrac{x^2+2x-x^2-x+2}{\left(x-2\right)\left(x+2\right)}=\dfrac{x+2}{\left(x-2\right)\left(x+2\right)}=\dfrac{1}{x-2}\)
11 tháng 1 2022
\(A=\dfrac{x}{x-2}+\dfrac{x^2+x-2}{4-x^2}\left(x\ne\pm2\right).\)
\(A=\dfrac{x}{x-2}-\dfrac{\left(x-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{x}{x-2}-\dfrac{x-1}{x-2}=\dfrac{x-x+1}{x-2}=\dfrac{1}{x-2.}\)
9 tháng 11 2021
a) \(\dfrac{x}{x-y}+\dfrac{2y^2}{x^2-y^2}-\dfrac{x}{x+y}=\dfrac{x\left(x+y\right)+2y^2-x\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}=\dfrac{x^2+xy+2y^2-x^2+xy}{\left(x-y\right)\left(x+y\right)}=\dfrac{2y^2+2xy}{\left(x-y\right)\left(x+y\right)}=\dfrac{2y\left(x+y\right)}{\left(x-y\right)\left(x+y\right)}=\dfrac{2y}{x-y}\)
b) \(B=\dfrac{x}{x-2}-\dfrac{4x}{x^2-4}-\dfrac{2}{x+2}=\dfrac{x\left(x+2\right)-4x-2\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{x^2+2x-4x-2x+4}{\left(x-2\right)\left(x+2\right)}=\dfrac{x^2-4x+4}{\left(x-2\right)\left(x+2\right)}=\dfrac{\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}=\dfrac{x-2}{x+2}\)
c) \(\dfrac{5}{x+1}-\dfrac{10}{-x^2+x-1}-\dfrac{15}{x^3+1}=\dfrac{5}{x+1}+\dfrac{10}{x^2-x+1}-\dfrac{15}{x^3+1}=\dfrac{5\left(x^2-x+1\right)+10\left(x+1\right)-15}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{5x^2-5x+5+10x+10-15}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{5x^2+5x}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{5x\left(x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{5x}{x^2-x+1}\)
21 tháng 10 2021
Bài 2:
Ta có: \(x\left(x-4\right)-x^2+8=0\)
\(\Leftrightarrow x^2-4x-x^2+8=0\)
\(\Leftrightarrow-4x=-8\)
hay x=2
12 tháng 4 2022
\(A=\dfrac{x+3}{\left(x-3\right)^2}:\dfrac{12-x^2+x+x^2-9}{x\left(x-3\right)}\)
\(=\dfrac{x+3}{\left(x-3\right)^2}\cdot\dfrac{x\left(x-3\right)}{x+3}=\dfrac{x}{x-3}\)
MN
2
6 tháng 11 2021
\(a,=6x^2-4x-x^2-4x-4=5x^2-8x-4\\ b,=x^3+8-2\left(1-x^2\right)=x^3+8-2+2x^2=x^3+2x^2+6\\ c,=\left(2x-1\right)^2-2\left(2x-1\right)\left(2x+1\right)+\left(2x+1\right)^2\\ =\left(2x+1-2x+1\right)^2=4\)
6 tháng 11 2021
Có thể giúp mình thực hiện cách chi tiết ko ạ ? Gv dạy mik ko hiểu mấy
A = -(x + 2)(x - 5) + (x - 1)(x - 2)
A = -x2 + 3x + 10 + x2 - 3x + 2
A = (-x2 + x2) + (3x - 3x) + 10 + 2
A = 12