Tính
a) \(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
b) \(2y+\dfrac{6xy+2y}{3x+2y}+\dfrac{2y-9x^2}{3x+2y}\)
Những câu hỏi liên quan
tính:
a, \(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
b, 2y - \(\dfrac{6xy+2y}{3x+2y}+\dfrac{2y-9x^2}{3x+2y}\)
Bài 1:Tìm đa thức M
a)\(\dfrac{^{x^3}+27}{x^2-3x+9}\)=\(\dfrac{x+3}{M}\)
b)\(\dfrac{M}{x+4}\)=\(\dfrac{x^2-8x+16}{16-x^2}\)
c)\(\dfrac{x-2y}{M}\)=\(\dfrac{3x^2-7xy+2y^2}{3x^2+5xy-2y^2}\)
a, \(\dfrac{x^3+27}{x^2-3x+9}=\dfrac{x+3}{M}\Leftrightarrow\dfrac{\left(x+3\right)\left(x^2-3x+9\right)}{x^2-3x+9}=\dfrac{x+3}{M}\)
\(\Rightarrow M=\dfrac{x+3}{x+3}=1\)
b, \(\dfrac{M}{x+4}=\dfrac{x^2-8x+16}{16-x^2}=\dfrac{\left(x-4\right)^2}{\left(4-x\right)\left(x+4\right)}=\dfrac{4-x}{x+4}\)
\(\Rightarrow M=\dfrac{\left(4-x\right)\left(x+4\right)}{x+4}=4-x\)
c, tương tự
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1 tháng 12 2021 lúc 7:29
\(\text{(12x^2y^2- 6xy^2) : 3xy+2y}\)
\(\text{b. \dfrac{4}{x+1} + \dfrac{8}{\left(x+1\right)\left(x-1\right)}}\)\(\text{c. \dfrac{1 }{x+1}- \dfrac{1}{x-1} +\dfrac{ 2x}{x^2-1}
}\)
\(a,\left(12x^2y^2-6xy^2\right):3xy+2y=6xy^2\left(2x-1\right):3xy+2y=2y\left(2x-1\right)+2y=4xy-2y+2y=4xy\)
\(b,\dfrac{4}{x+1} + \dfrac{8}{\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{4\left(x-1\right)+8}{\left(x+1\right)\left(x-1\right)}\\ =\dfrac{4x-4+8}{\left(x+1\right)\left(x-1\right)}\\ =\dfrac{4x+4}{\left(x+1\right)\left(x-1\right)}\\ =\dfrac{4\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}=\dfrac{4}{x-1}\)
\(c,\dfrac{1 }{x+1}- \dfrac{1}{x-1} +\dfrac{ 2x}{x^2-1} \)
\(=\dfrac{x-1}{\left(x+1\right)\left(x-1\right)}-\dfrac{x+1}{\left(x+1\right)\left(x-1\right)}+\dfrac{2x}{\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{x-1-x-1+2x}{\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{2x-2}{\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{2\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{2}{x+1}\)
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\(a,=4xy-2y+2y=4xy\\ b,\dfrac{4}{x+1}+\dfrac{8}{\left(x+1\right)\left(x-1\right)}=\dfrac{4x-4+8}{\left(x+1\right)\left(x-1\right)}\\ =\dfrac{4x+4}{\left(x+1\right)\left(x-1\right)}=\dfrac{4\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{4}{x-1}\\ c,\dfrac{1}{x+1}-\dfrac{1}{x-1}+\dfrac{2x}{x^2-1}=\dfrac{x-1-x-1+2x}{\left(x-1\right)\left(x+1\right)}\\ =\dfrac{2x-2}{\left(x-1\right)\left(x+1\right)}=\dfrac{2\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{2}{x+1}\)
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thực hiện các phép tính sau
a)\(\dfrac{x+1}{2x+6}+\dfrac{2x+3}{x^2+3x}\)
b)\(\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)
c)\(\dfrac{x}{x-2y}+\dfrac{x}{x+2y}+\dfrac{4xy}{4y^2-x^2}\)
d)\(\dfrac{1}{3x-2}-\dfrac{1}{3x+2}-\dfrac{3x-6}{4-9x^2}\)
Thực hiện phép tính:
a) \(\dfrac{x}{2x-y}-\dfrac{2x-y}{4x-2y}\)
b)\(\dfrac{3x+1}{x^2-1}-\dfrac{x}{2x-2}\)
c) \(\dfrac{x-2}{x^2-4}-\dfrac{-8-x}{3x^2+6x}\)
d) \(\dfrac{2}{2x-3}-\dfrac{x}{2x+3}-\dfrac{2x+1}{9-4x^2}\)
a: \(=\dfrac{2x-2x+y}{2\left(2x-y\right)}=\dfrac{y}{2\left(2x-y\right)}\)
b: \(=\dfrac{3x+1}{\left(x-1\right)\left(x+1\right)}-\dfrac{x}{2\left(x-1\right)}\)
\(=\dfrac{6x+2-x^2-x}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{-x^2+5x+2}{2\left(x-1\right)\left(x+1\right)}\)
c: \(=\dfrac{1}{x+2}+\dfrac{x+8}{3x\left(x+2\right)}\)
\(=\dfrac{3x+x+8}{3x\left(x+2\right)}=\dfrac{4x+8}{3x\left(x+2\right)}=\dfrac{4}{3x}\)
d: \(=\dfrac{4x+6-2x^2+3x+2x+1}{\left(2x-3\right)\left(2x+3\right)}\)
\(=\dfrac{-2x^2+9x+7}{\left(2x-3\right)\left(2x+3\right)}\)
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bài 11.rút gọn biểu thức:a,dfrac{9x^2}{11y^2}:dfrac{3x}{2y}:dfrac{6x}{11y} b,dfrac{3x+15y}{x^3-y^3}:dfrac{x+5y}{x-y} c,dfrac{x^2-1}{x^2-4x+4}:dfrac{x+1}{2-x} d,dfrac{5x+10}{x+2}:dfrac{5y}{x} e,dfrac{2x}{3x-3y}:dfrac{x^2}{x-y} f,dfrac{5x-3}{4x^2y}-dfrac{x-3}{4x^2y} g,dfrac{3x+10}{x+3}-dfrac{x+4}{x+3} h,dfrac{4}{x-1}+dfrac{2}{1-x}+dfrac{x}{x-1} i,dfrac{2x^2-x}{x-1}+dfrac{x+1}{1-x}+dfrac{2-x^2}{x-1} j,dfrac{x-2}{x-6}-d...
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bài 11.rút gọn biểu thức:
\(a,\dfrac{9x^2}{11y^2}:\dfrac{3x}{2y}:\dfrac{6x}{11y}\) \(b,\dfrac{3x+15y}{x^3-y^3}:\dfrac{x+5y}{x-y}\)
\(c,\dfrac{x^2-1}{x^2-4x+4}:\dfrac{x+1}{2-x}\) \(d,\dfrac{5x+10}{x+2}:\dfrac{5y}{x}\)
\(e,\dfrac{2x}{3x-3y}:\dfrac{x^2}{x-y}\) \(f,\dfrac{5x-3}{4x^2y}-\dfrac{x-3}{4x^2y}\)
\(g,\dfrac{3x+10}{x+3}-\dfrac{x+4}{x+3}\) \(h,\dfrac{4}{x-1}+\dfrac{2}{1-x}+\dfrac{x}{x-1}\)
\(i,\dfrac{2x^2-x}{x-1}+\dfrac{x+1}{1-x}+\dfrac{2-x^2}{x-1}\) \(j,\dfrac{x-2}{x-6}-\dfrac{x-18}{6-x}+\dfrac{x+2}{x-6}\)
\(k,\dfrac{x}{x^2-4}+\dfrac{2}{2-x}+\dfrac{1}{x+2}\) \(m,\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)
\(n,\dfrac{3}{x+3}-\dfrac{x-6}{x^2+3x}\) \(p,\dfrac{x+3}{x}-\dfrac{x}{x-3}+\dfrac{9}{x^2-3x}\)
f: \(=\dfrac{5x-3-x+3}{4x^2y}=\dfrac{4x}{4x^2y}=\dfrac{1}{xy}\)
g: \(=\dfrac{3x+10-x-4}{x+3}=\dfrac{2x+6}{x+3}=2\)
h: \(=\dfrac{4-2+x}{x-1}=\dfrac{x+2}{x-1}\)
n: \(=\dfrac{3x-x+6}{x\left(x+3\right)}=\dfrac{2\left(x+3\right)}{x\left(x+3\right)}=\dfrac{2}{x}\)
p: \(=\dfrac{x^2-9-x^2+9}{x\left(x-3\right)}=0\)
k: \(=\dfrac{x-2x-4+x-2}{\left(x+2\right)\left(x-2\right)}=\dfrac{-6}{x^2-4}\)
m: \(=\dfrac{3x-x+6}{x\left(2x+6\right)}=\dfrac{2x+6}{x\left(2x+6\right)}=\dfrac{1}{x}\)
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Mọi người giải nhanh bài này giúp mình với, mình sắp phải nộp bài rồi😓
Thực hiện phép tính sau:
1. dfrac{2x+6}{3x^2-x}:dfrac{x^2+3x}{1-3x}
2. dfrac{x}{x-2y}+dfrac{x}{x+2y}+dfrac{4xy}{4y^2-x^2}
3. dfrac{1}{3x-2}-dfrac{1}{3x+2}-dfrac{3x-6}{4-9x^2}
4.dfrac{x+3}{x+1}+dfrac{2x-1}{x-1}+dfrac{x+5}{x^2-1}
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Mọi người giải nhanh bài này giúp mình với, mình sắp phải nộp bài rồi😓
Thực hiện phép tính sau:
1. \(\dfrac{2x+6}{3x^2-x}:\dfrac{x^2+3x}{1-3x}\)
2. \(\dfrac{x}{x-2y}+\dfrac{x}{x+2y}+\dfrac{4xy}{4y^2-x^2}\)
3. \(\dfrac{1}{3x-2}-\dfrac{1}{3x+2}-\dfrac{3x-6}{4-9x^2}\)
4.\(\dfrac{x+3}{x+1}+\dfrac{2x-1}{x-1}+\dfrac{x+5}{x^2-1}\)
Thực hiện các phép tính :
a) left(dfrac{9}{x^3-9x}+dfrac{1}{x+3}right):left(dfrac{x-3}{x^2+3x}-dfrac{x}{3x+9}right)
b) left(dfrac{2}{x-2}-dfrac{2}{x+2}right).dfrac{x^2+4x+4}{8}
c) left(dfrac{3x}{1-3x}+dfrac{2x}{3x+1}right):dfrac{6x^2+10x}{1-6x+9x^2}
d) left(dfrac{x}{x^2-25}-dfrac{x-5}{x^2+5x}right):dfrac{2x-5}{x^2+5x}+dfrac{x}{5-x}
e) left(dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+dfrac{y}{x^2+y^2}right):left(dfrac{1}{x-y}-dfrac{2xy}{x^3-x^2y+xy^2-y^3}right)
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Thực hiện các phép tính :
a) \(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)
b) \(\left(\dfrac{2}{x-2}-\dfrac{2}{x+2}\right).\dfrac{x^2+4x+4}{8}\)
c) \(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
d) \(\left(\dfrac{x}{x^2-25}-\dfrac{x-5}{x^2+5x}\right):\dfrac{2x-5}{x^2+5x}+\dfrac{x}{5-x}\)
e) \(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^3-x^2y+xy^2-y^3}\right)\)
giải hệ pt :
a, \(\left\{{}\begin{matrix}3xy+2y=5\\2xy\left(x+y\right)+y^2=5\end{matrix}\right.\)
b, \(\left\{{}\begin{matrix}\dfrac{1}{x}-\dfrac{1}{2y}=2\left(y^4-x^4\right)\\\dfrac{1}{x}+\dfrac{1}{2y}=\left(3y^2+x^2\right)\left(3x^2+y^2\right)\end{matrix}\right.\)
a.
Với \(y=0\) không phải nghiệm
Với \(y\ne0\Rightarrow\left\{{}\begin{matrix}3x+2=\dfrac{5}{y}\\2x\left(x+y\right)+y=\dfrac{5}{y}\end{matrix}\right.\)
\(\Rightarrow3x+2=2x\left(x+y\right)+y\)
\(\Leftrightarrow2x^2+\left(2y-3\right)x+y-2=0\)
\(\Delta=\left(2y-3\right)^2-8\left(y-2\right)=\left(2y-5\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{-2y+3+2y-5}{4}=-\dfrac{1}{2}\\x=\dfrac{-2y+3-2y+5}{4}=-y+2\end{matrix}\right.\)
Thế vào pt đầu ...
Câu b chắc chắn đề sai
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