Rút gọn: (x+2)/(x^2-4x+4) : ((6-x^2/x^2-2x) - (1/2-x) +(x+2/x))
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Những câu hỏi liên quan
22 tháng 10 2023
1:
a: \(\left(2x-5\right)^2-4x\left(x+3\right)\)
\(=4x^2-20x+25-4x^2-12x\)
=-32x+25
b: \(\left(x-2\right)^3-6\left(x+4\right)\left(x-4\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
\(=x^3-6x^2+12x-8-\left(x^3-8\right)-6\left(x^2-16\right)\)
\(=-6x^2+12x-6x^2+96=-12x^2+12x+96\)
c: \(\left(x-1\right)^2-2\left(x-1\right)\left(x+2\right)+\left(x+2\right)^2+5\left(2x-3\right)\)
\(=\left(x-1-x-2\right)^2+5\left(2x-3\right)\)
\(=\left(-3\right)^2+5\left(2x-3\right)\)
\(=9+10x-15=10x-6\)
2:
a: \(\left(2-3x\right)^2-5x\left(x-4\right)+4\left(x-1\right)\)
\(=9x^2-12x+4-5x^2+20x+4x-4\)
\(=4x^2+12x\)
b: \(\left(3-x\right)\left(x^2+3x+9\right)+\left(x-3\right)^3\)
\(=27-x^3+x^3-9x^2+27x-27\)
\(=-9x^2+27x\)
c: \(\left(x-4\right)^2\left(x+4\right)-\left(x-4\right)\left(x+4\right)^2+3\left(x^2-16\right)\)
\(=\left(x-4\right)\left(x+4\right)\left(x-4-x-4\right)+3\left(x^2-16\right)\)
\(=\left(x^2-16\right)\left(-8\right)+3\left(x^2-16\right)\)
\(=-5\left(x^2-16\right)=-5x^2+80\)
TK
1
18 tháng 12 2021
\(a,=\dfrac{\left(x+1\right)^2}{x\left(x+1\right)}=\dfrac{x+1}{x}\\ b,=\dfrac{-\left(x^2-5x-6\right)}{\left(x+2\right)^2}=\dfrac{-\left(x+1\right)\left(x-6\right)}{\left(x+2\right)^2}\)
PT
21 tháng 7 2021
a/ 2x\(^{^{ }3}\)-3\(^{^{ }3}\)-2x\(^3\)-1\(^{^{ }3}\)=-28
b/x\(^{^{ }3}\)+2\(^{^{ }3}\)-x\(^3\)+2=10
c/3x\(^3\)+5\(^3\)-3x(3x\(^2\)-1)=3x\(^3\)+5\(^3\)-3x\(^3\)+3x=125+3x
d/ x\(^6\)-(x\(^3\)+1)(x\(^2\)-x+1)= x\(^6\)-(x\(^6\)-x\(^4\)+x\(^3\)+x\(^2\)-x+1)=x\(^4\)-x\(^3\)-x\(^2\)+x-1
H9
HT.Phong (9A5)
CTVHS
26 tháng 10 2023
a) \(\dfrac{2\left(x+1\right)^2}{4x\left(x+1\right)}\left(x\ne0;x\ne-1\right)\)
\(=\dfrac{2\left(x+1\right)^2:2\left(x+1\right)}{4x\left(x+1\right):2\left(x+1\right)}\)
\(=\dfrac{x+1}{2x}\)
b) \(\dfrac{\left(8-x\right)\left(-x-2\right)}{\left(x+2\right)^2}\left(x\ne-2\right)\)
\(=\dfrac{-\left(8-x\right)\left(x+2\right)}{\left(x+2\right)^2}\)
\(=\dfrac{-\left(8-x\right)}{x+2}\)
\(=\dfrac{x-8}{x+2}\)
c) \(\dfrac{2\left(x-y\right)}{y-x}\left(x\ne y\right)\)
\(=\dfrac{2\left(x-y\right)}{-\left(x-y\right)}\)
\(=-2\)
d) \(\dfrac{\left(x+2\right)^2}{2x+4}\left(x\ne-2\right)\)
\(=\dfrac{\left(x+2\right)^2}{2\left(x+2\right)}\)
\(=\dfrac{x+2}{2}\)
T
26 tháng 10 2023
ĐKXĐ: \(x\neq0;x\neq-1\)
\(\dfrac{2(x+1)^2}{4x(x+1)}=\dfrac{2(x+1)}{4x}=\dfrac{x+1}{2x}\)
$---$
ĐKXĐ: \(x\neq-2\)
\(\dfrac{(8-x)(-x-2)}{(x+2)^2}=\dfrac{-(8-x)(x+2)}{(x+2)^2}=\dfrac{x-8}{x+2}\)
$---$
ĐKXĐ: \(x\neq y\)
\(\dfrac{2(x-y)}{y-x}=\dfrac{-2(y-x)}{y-x}=-2\)
$---$
ĐKXĐ: \(x\neq-2\)
\(\dfrac{(x+2)^2}{2x+4}=\dfrac{(x+2)^2}{2(x+2)}=\dfrac{x+2}{2}\)
NM
1
5 tháng 12 2015
\(y=\frac{\frac{^x}{x^2}-x-6-x-\frac{1}{3}x^2-4x-15}{x^4}-2x^2+\frac{1}{3}x^2+11x+10b\)
\(y=\frac{-\left(5x^7-33x^6-30bx^5+x^3+18x^2+63x-3\right)}{3x^5}\)
JW
15 tháng 6 2016
Nhìn ko hiểu dâu "|" là dấu ngoặc hay dấu giá trị tuyệt đối
Bạn ghi rõ đề bài ra nha 
15 tháng 6 2016
cái này || ko phải là dấu tuyệt đối đâu mà là phép nhân, chia giua 2 phân số
22 tháng 11 2017
1, a,= (x+2)^2/3.(x+2) = x+2/3
b, = 3x.(x+4)/2x.(x+4) = 3/2
k mk nha
H
1
16 tháng 5 2022
a: \(P=\left(\dfrac{3}{2\left(x+2\right)}-\dfrac{x}{x-2}+\dfrac{2x^2+3}{\left(x-2\right)\left(x+2\right)}\right)\cdot\dfrac{4\left(x-2\right)}{2x-1}\)
\(=\left(\dfrac{3\left(x-2\right)}{2\left(x+2\right)\left(x-2\right)}-\dfrac{2x\left(x+2\right)}{2\left(x-2\right)\left(x+2\right)}+\dfrac{4x^2+6}{2\left(x-2\right)\left(x+2\right)}\right)\cdot\dfrac{4\left(x-2\right)}{2x-1}\)
\(=\dfrac{3x-6-2x^2-4x+4x^2+6}{2\left(x+2\right)\left(x-2\right)}\cdot\dfrac{4\left(x-2\right)}{2x-1}\)
\(=\dfrac{2x^2-x}{x+2}\cdot\dfrac{2}{2x-1}=\dfrac{2x}{x+2}\)
b: Khi 4x2-1=0 thì (2x-1)(2x+1)=0
=>x=1/2(loại) và x=-1/2(nhận)
Khi x=-1/2 thì \(P=\left(2\cdot\dfrac{-1}{2}\right):\left(-\dfrac{1}{2}+2\right)=-1:\dfrac{3}{2}=-\dfrac{2}{3}\)
H
1
2
16 tháng 5 2022
Với `x \ne +-2,x \ne 1/2,x \ne0`. Ta có:
`(3/[2x+4]+x/[2-x]+[2x^2+3]/[x^2-4]):[2x-1]/[4x-8]`
`=(3/[2(x+2)]-x/[x-2]+[2x^2+3]/[(x-2)(x+2)]).[4(x-2)]/[2x-1]`
`=[3(x-2)-2x(x+2)+2(2x^2+3)]/[x(x-2)(x+2)].[4(x-2)]/[2x-1]`
`=[3x-6-2x^2-4x+4x^2+6]/[x(x+2)]. 4/[2x-1]`
`=[2x^2-x]/[x(x+2)]. 4/[2x-1]`
`=[x(2x-1)]/[x(x+2)] . 4/[2x-1]`
`=4/[x+2]`
\(=\dfrac{x+2}{\left(x-2\right)^2}:\left(\dfrac{6-x^2+x+x^2-4}{x\left(x-2\right)}\right)\)
\(=\dfrac{x+2}{\left(x-2\right)^2}\cdot\dfrac{x\left(x-2\right)}{x+2}=\dfrac{x}{x-2}\)