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\(C=\dfrac{x^3}{x^2-4}-\dfrac{x}{x-2}+\dfrac{2}{x+2}\)

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

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

\(=\dfrac{x^3-x^2-4}{x^2-4}\)

a,\(C=\dfrac{x^3}{x^2-4}-\dfrac{x}{x-2}-\dfrac{2}{x+2}\)

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

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

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

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

\(\Rightarrow C=\dfrac{x^2\left(x-1\right)-4\left(x-1\right)}{\left(x-2\right)\left(x+2\right)}\)

\(\Rightarrow C=\dfrac{\left(x^2-4\right)\left(x-1\right)}{\left(x-2\right)\left(x+2\right)}\)

\(\Rightarrow C=\dfrac{\left(x-2\right)\left(x+2\right)\left(x-1\right)}{\left(x-2\right)\left(x+2\right)}\)

\(\Rightarrow C=x-1\)

b, C=0\(\Rightarrow x-1=0\Rightarrow x=1\)

c, Để C nhận giá trị dương thì \(x-1\ge0\Rightarrow x\ge1\)

a: Xét (O) có

BC là đường kính

DE là dây

=>DE<BC

b: Xét ΔOBD có OB=OD và góc B=60 độ

nên ΔOBD đều

c: Xét (O) có

ΔBDC nội tiếp

BC là đường kính

Do đó: ΔBDC vuông tại D

=>CD vuông góc với AB

mà ΔBCA đều

nên D là trung điểm của AB

Xet (O) có

ΔBEC nội tiếp

BC là đường kính

Do đó: ΔBEC vuông tại E

=>BE vuông góc với AC

mà ΔBAC đều

nên E là trung điểm của AC

Xét ΔABC có AD/AB=AE/AC

nên DE//BC

\(M=\frac{3}{2}+\frac{3}{6}+\frac{3}{12}+...+\frac{3}{2021.2022}\)

    \(=3\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2021.2022}\right)\)

    \(=3\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2021}-\frac{1}{2022}\right)\)

    \(=3\left(1-\frac{1}{2022}\right)\)

    \(=3.\frac{2021}{2022}\)

    \(=\frac{6063}{2022}\)

A =  3+ (3 + 3 + 3 + 3 ) : ( 10 + 100 + 1000 + 10000 + 100000 )

A=  3 + (12 : 111111)

A = 3 + 4/37037

A = 3,000108

\(\frac{10}{3}=3,33333333333>3,000108\)

=> A nhỏ hơn

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Among many programs and channels available on TV these days such as the current news programs, sport programs, entertaining programs, educational programs and movie programs, etc, I the program "the World of Animals" most.

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4:

a: 7/10

b: 6/5=12/10

7/2=35/10

8/25=32/100

11/50=22/100

23/125=204/1000

17/20=85/100

41/200=205/1000