Tính :\(\dfrac{x+1}{x-1}-\dfrac{x_{ }-1}{x+1}\), Chọn đáp án đúng
A.\(\dfrac{-4x}{x^2-1}\) B.\(\dfrac{2\left(x+1\right)}{x-1}\) C.\(\dfrac{2\left(x^2+1\right)}{x^2-1}\) D. \(\dfrac{4x}{x^2-1}\)
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1. Đáp án nào đúng: a) dfrac{3x}{5y}dfrac{3xleft(x-2right)}{5yleft(x-2right)}b) dfrac{3x}{5y}dfrac{2xleft(x-2right)}{3yleft(x+2right)}c) dfrac{3x}{5y}dfrac{9x}{15y}d) dfrac{3x}{5y}dfrac{3x.x}{5y.x}2. Tìm đa thức M trong đẳng thức dfrac{8left(x-yright)}{4left(x^2-y^2right)} dfrac{ }{x+y}3. Rút gọn phân thức dfrac{6x^2y^3}{8x^3y^3}4. Rút gọn phân thức dfrac{20xyleft(x+yright)}{5xyleft(x-yright)}5. Rút gọn phân thức dfrac{6x-12}{left(x+3right)left(x-3right)}6. Rút gọn phân thức dfrac{4left(x-1right...
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1. Đáp án nào đúng:
a) \(\dfrac{3x}{5y}=\dfrac{3x\left(x-2\right)}{5y\left(x-2\right)}\)
b) \(\dfrac{3x}{5y}=\dfrac{2x\left(x-2\right)}{3y\left(x+2\right)}\)
c) \(\dfrac{3x}{5y}=\dfrac{9x}{15y}\)
d) \(\dfrac{3x}{5y}=\dfrac{3x.x}{5y.x}\)
2. Tìm đa thức M trong đẳng thức \(\dfrac{8\left(x-y\right)}{4\left(x^2-y^2\right)}\)= \(\dfrac{ }{x+y}\)
3. Rút gọn phân thức \(\dfrac{6x^2y^3}{8x^3y^3}=\)
4. Rút gọn phân thức \(\dfrac{20xy\left(x+y\right)}{5xy\left(x-y\right)}=\)
5. Rút gọn phân thức \(\dfrac{6x-12}{\left(x+3\right)\left(x-3\right)}=\)
6. Rút gọn phân thức \(\dfrac{4\left(x-1\right)-2\left(1-x\right)}{6\left(x-1\right)}=\)
giúp mình nhé mng mình đang gấp ạ
1A,B,D
2 M=2
3 \(=\dfrac{3}{4x}\)
4 \(=\dfrac{4\left(x+y\right)}{x-y}=\dfrac{4x+4y}{x-y}\)
5 K rút gọn đc
6 \(=\dfrac{4\left(x-1\right)+2\left(x-1\right)}{6\left(x-1\right)}=\dfrac{6\left(x-1\right)}{6\left(x-1\right)}=1\)
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Làm các phép tính sau :
a) \(\dfrac{y}{2x^2-xy}+\dfrac{4x}{y^2-2xy}\)
b) \(\dfrac{1}{x+2}+\dfrac{3}{x^2-4}+\dfrac{x-14}{\left(x^2+4x+4\right)\left(x-2\right)}\)
c) \(\dfrac{1}{x+2}+\dfrac{1}{\left(x+2\right)\left(4x+7\right)}\)
d) \(\dfrac{1}{x+3}+\dfrac{1}{\left(x+3\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(4x+7\right)}\)
chứng minh rằng :
a) left(dfrac{x^2-2x}{2x^2+8}-dfrac{2x^2}{8-4x+2x^2-x}right)left(1-dfrac{1}{x}-dfrac{2}{x^2}right)dfrac{x+1}{2x}
b)left[dfrac{2}{3x}-dfrac{2}{x+1}left(dfrac{x+1}{3x}-x-1right)right]:dfrac{x+1}{x}dfrac{2x}{x-1}
c)left[dfrac{2}{left(x+1right)^3}left(dfrac{1}{x}+1right)+dfrac{1}{x^2+2x+1}left(dfrac{1}{x^2}+1right)right]:dfrac{x-1}{x^3}dfrac{x}{x-1}
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chứng minh rằng :
a) \(\left(\dfrac{x^2-2x}{2x^2+8}-\dfrac{2x^2}{8-4x+2x^2-x}\right)\left(1-\dfrac{1}{x}-\dfrac{2}{x^2}\right)=\dfrac{x+1}{2x}\)
b)\(\left[\dfrac{2}{3x}-\dfrac{2}{x+1}\left(\dfrac{x+1}{3x}-x-1\right)\right]:\dfrac{x+1}{x}=\dfrac{2x}{x-1}\)
c)\(\left[\dfrac{2}{\left(x+1\right)^3}\left(\dfrac{1}{x}+1\right)+\dfrac{1}{x^2+2x+1}\left(\dfrac{1}{x^2}+1\right)\right]:\dfrac{x-1}{x^3}=\dfrac{x}{x-1}\)
b: \(=\left[\dfrac{2}{3x}-\dfrac{2}{x+1}\cdot\dfrac{x+1-3x^2-3x}{3x}\right]\cdot\dfrac{x}{x+1}\)
\(=\left(\dfrac{2}{3x}-\dfrac{2}{x+1}\cdot\dfrac{-3x^2-2x+1}{3x}\right)\cdot\dfrac{x}{x+1}\)
\(=\dfrac{2x+2+6x^2+4x-2}{3x\left(x+1\right)}\cdot\dfrac{x}{x+1}\)
\(=\dfrac{6x^2+6x}{3\left(x+1\right)}\cdot\dfrac{1}{x+1}\)
\(=\dfrac{6x\left(x+1\right)}{3\left(x+1\right)^2}=\dfrac{2x}{x+1}\)
c: \(VT=\left[\dfrac{2}{\left(x+1\right)^3}\cdot\dfrac{x+1}{x}+\dfrac{1}{\left(x+1\right)^2}\cdot\dfrac{1+x^2}{x^2}\right]\cdot\dfrac{x^3}{x-1}\)
\(=\left(\dfrac{2}{x\left(x+1\right)^2}+\dfrac{x^2+1}{x^2\cdot\left(x+1\right)^2}\right)\cdot\dfrac{x^3}{x-1}\)
\(=\dfrac{2x+x^2+1}{x^2\cdot\left(x+1\right)^2}\cdot\dfrac{x^3}{x-1}\)
\(=\dfrac{\left(x+1\right)^2}{\left(x+1\right)^2}\cdot\dfrac{x}{x-1}=\dfrac{x}{x-1}\)
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Làm các phép tính sau :
a) \(\left(\dfrac{x^2}{y^2}+\dfrac{y}{x}\right):\left(\dfrac{x}{y^2}-\dfrac{1}{y}+\dfrac{1}{x}\right)\)
b) \(\left(\dfrac{1}{x^2+4x+4}-\dfrac{1}{x^2-4x+4}\right):\left(\dfrac{1}{x+2}-\dfrac{1}{x-2}\right)\)
a) dfrac{x^2-x}{x-2}+dfrac{4-3x}{x-2}
b) dfrac{a+2b}{3a-b}+dfrac{2a-5b}{b-3a}
c) dfrac{2}{x^2-9}+dfrac{1}{x+3}
d) dfrac{4x}{x^2-4}+dfrac{x}{x+2}+dfrac{2}{x-2}
e) dfrac{3x^2-x+3}{x^3-1}+dfrac{1-x}{x^2+x+1}+dfrac{2}{1-x}
f) dfrac{1}{x^2+3x+2}+dfrac{1-x}{x^2+x+1}+dfrac{2}{1-x}
g) dfrac{a^3}{left(a-bright)left(a-cright)}+dfrac{b^3}{left(b-aright)left(b-cright)}+dfrac{c^3}{left(c-aright)left(c-bright)}
h) dfrac{1}{1-x}+dfrac{1}{1+x}+dfrac{2}{1+x^2}+dfrac{4}{1+x^4}+dfrac{8}{1+x^8}
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a) \(\dfrac{x^2-x}{x-2}+\dfrac{4-3x}{x-2}\)
b) \(\dfrac{a+2b}{3a-b}+\dfrac{2a-5b}{b-3a}\)
c) \(\dfrac{2}{x^2-9}+\dfrac{1}{x+3}\)
d) \(\dfrac{4x}{x^2-4}+\dfrac{x}{x+2}+\dfrac{2}{x-2}\)
e) \(\dfrac{3x^2-x+3}{x^3-1}+\dfrac{1-x}{x^2+x+1}+\dfrac{2}{1-x}\)
f) \(\dfrac{1}{x^2+3x+2}+\dfrac{1-x}{x^2+x+1}+\dfrac{2}{1-x}\)
g) \(\dfrac{a^3}{\left(a-b\right)\left(a-c\right)}+\dfrac{b^3}{\left(b-a\right)\left(b-c\right)}+\dfrac{c^3}{\left(c-a\right)\left(c-b\right)}\)
h) \(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}\)
a, \(\dfrac{x^2-x}{x-2}+\dfrac{4-3x}{x-2}\)
\(=\dfrac{x^2-x+4-3x}{x-2}=\dfrac{x^2-4x+4}{x-2}\)
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c) \(\dfrac{2}{x^2-9}+\dfrac{1}{x+3}\)
Ta có: \(\dfrac{1}{x+3}=\dfrac{1\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}=\dfrac{x-3}{x^2-9}\)
\(\Rightarrow\dfrac{2}{x^2-9}+\dfrac{1}{x+3}=\dfrac{2}{x^2-9}+\dfrac{x-3}{x^2-9}=\dfrac{2+x-3}{x^2-9}=\dfrac{x-1}{x^2-9}\)
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b: \(=\dfrac{a+2b}{3a-b}-\dfrac{2a-5b}{3a-b}\)
\(=\dfrac{a+2b-2a+5b}{3a-b}=\dfrac{-a+7b}{3a-b}\)
c: \(=\dfrac{2+x-3}{\left(x+3\right)\left(x-3\right)}=\dfrac{x+1}{\left(x+3\right)\left(x-3\right)}\)
d: \(=\dfrac{4x+x^2-2x+2x+4}{\left(x+2\right)\left(x-2\right)}=\dfrac{x^2+4x+4}{\left(x+2\right)\left(x-2\right)}=\dfrac{x+2}{x-2}\)
e: \(=\dfrac{3x^2-x+3+1-2x+x^2-2x^2-2x-2}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\dfrac{2x^2-5x+2}{\left(x-1\right)\left(x^2+x+1\right)}\)
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Giải các phương trình sau :
a) dfrac{1-6x}{x-2}+dfrac{9x+4}{x+2}dfrac{xleft(3x-2+1right)}{x^2-4}
b) 1+dfrac{x}{3-x}dfrac{5x}{left(x+2right)left(3-xright)}+dfrac{2}{x+2}
c) dfrac{2}{x-1}+dfrac{2x+3}{x^2+x+1}dfrac{left(2x-1right)left(2x+1right)}{x^3-1}
d) dfrac{x^3-left(x-1right)^3}{left(4x+3right)left(x-5right)}dfrac{7x-1}{4x+3}-dfrac{x}{x-5}
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Giải các phương trình sau :
a) \(\dfrac{1-6x}{x-2}+\dfrac{9x+4}{x+2}=\dfrac{x\left(3x-2+1\right)}{x^2-4}\)
b) \(1+\dfrac{x}{3-x}=\dfrac{5x}{\left(x+2\right)\left(3-x\right)}+\dfrac{2}{x+2}\)
c) \(\dfrac{2}{x-1}+\dfrac{2x+3}{x^2+x+1}=\dfrac{\left(2x-1\right)\left(2x+1\right)}{x^3-1}\)
d) \(\dfrac{x^3-\left(x-1\right)^3}{\left(4x+3\right)\left(x-5\right)}=\dfrac{7x-1}{4x+3}-\dfrac{x}{x-5}\)
Tính
a)left(dfrac{left(x-1right)^2}{left(3x+x-1right)^2}-dfrac{1-2x^2+4x}{x^3-1}+dfrac{1}{x-1}right):dfrac{x^2+x}{x^2+1}
b)left(dfrac{3left(x+2right)}{2left(x^3+x^2+x+1right)}+dfrac{2x^2-x+10}{2left(x^3+x^2+x+1right)}right):left(dfrac{5}{x^2+1}+dfrac{3}{2left(x+1right)}-dfrac{3}{2left(x-1right)}right).dfrac{2}{x-1}
c)left(dfrac{x^2}{x^2-5x+6}+dfrac{x^2}{x^2-3x+2}right):dfrac{left(x-1right)left(x-3right)}{x^4+x^2+1}
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Tính
a)\(\left(\dfrac{\left(x-1\right)^2}{\left(3x+x-1\right)^2}-\dfrac{1-2x^2+4x}{x^3-1}+\dfrac{1}{x-1}\right):\dfrac{x^2+x}{x^2+1}\)
b)\(\left(\dfrac{3\left(x+2\right)}{2\left(x^3+x^2+x+1\right)}+\dfrac{2x^2-x+10}{2\left(x^3+x^2+x+1\right)}\right):\left(\dfrac{5}{x^2+1}+\dfrac{3}{2\left(x+1\right)}-\dfrac{3}{2\left(x-1\right)}\right).\dfrac{2}{x-1}\)
c)\(\left(\dfrac{x^2}{x^2-5x+6}+\dfrac{x^2}{x^2-3x+2}\right):\dfrac{\left(x-1\right)\left(x-3\right)}{x^4+x^2+1}\)
Giải các pt sau:
a)x^2+dfrac{4x^2}{left(x+2right)^2}12
b) dfrac{x^2}{3}+dfrac{48}{x^2}5left(dfrac{x}{3}+dfrac{4}{x}right)
c) left(dfrac{x}{x-1}right)^2+left(dfrac{x}{x+1}right)^2dfrac{10}{9}
d) left(dfrac{x-1}{x}right)^2+left(dfrac{x-1}{x-2}right)^2dfrac{40}{9}
e) x^2+left(dfrac{x}{x-1}right)^28
g) x^3+dfrac{1}{x^3}6left(x+dfrac{1}{x}right)
f) left(x^2+dfrac{1}{x^2}right)+5left(x+dfrac{1}{x}right)-120
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Giải các pt sau:
a)\(x^2+\dfrac{4x^2}{\left(x+2\right)^2}=12\)
b) \(\dfrac{x^2}{3}+\dfrac{48}{x^2}=5\left(\dfrac{x}{3}+\dfrac{4}{x}\right)\)
c) \(\left(\dfrac{x}{x-1}\right)^2+\left(\dfrac{x}{x+1}\right)^2=\dfrac{10}{9}\)
d) \(\left(\dfrac{x-1}{x}\right)^2+\left(\dfrac{x-1}{x-2}\right)^2=\dfrac{40}{9}\)
e) \(x^2+\left(\dfrac{x}{x-1}\right)^2=8\)
g) \(x^3+\dfrac{1}{x^3}=6\left(x+\dfrac{1}{x}\right)\)
f) \(\left(x^2+\dfrac{1}{x^2}\right)+5\left(x+\dfrac{1}{x}\right)-12=0\)
Thực hiện các phép tính sau :
a) \(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
b) \(\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
c) \(\dfrac{1}{x-1}-\dfrac{x^3-x}{x^2+1}.\left(\dfrac{1}{x^2-2x+1}+\dfrac{1}{1-x^2}\right)\)
a) (2x+12x−1−2x−12x+1):4x10x−5=(2x+1)2−(2x−1)2(2x−1)(2x+1).10x+54x(2x+12x−1−2x−12x+1):4x10x−5=(2x+1)2−(2x−1)2(2x−1)(2x+1).10x+54x
=4x2+4x+1−4x2+4x−1(2x−1)(2x+1).5(2x+1)4x4x2+4x+1−4x2+4x−1(2x−1)(2x+1).5(2x+1)4x
=8x.5(2x+1)(2x−1)(2
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b) \(\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)=\left(\dfrac{1}{x\left(x+1\right)}-\dfrac{x\left(2-x\right)}{x\left(x+1\right)}\right):\left(\dfrac{1}{x}+\dfrac{x^2}{x}-\dfrac{2x}{x}\right)=\left(\dfrac{1-2x+x^2}{x\left(x+1\right)}\right):\left(\dfrac{1+x^2-2x}{x}\right)=\left(\dfrac{\left(x-1\right)^2}{x\left(x+1\right)}\right)\cdot\left(\dfrac{x}{\left(x-1\right)^2}\right)=\dfrac{\left(x-1\right)^2\cdot x}{\left(x-1\right)^2\cdot x\cdot\left(x+1\right)}=\dfrac{1}{x+1}\)
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c) nè
\(\dfrac{1}{x-1}-\dfrac{x^3-x}{x^2+1}\cdot\left(\dfrac{1}{x^2-2x+1}+\dfrac{1}{1-x^2}\right)\)
\(=\dfrac{1}{x-1}-\dfrac{x\left(x^2-1\right)}{x^2+1}\cdot\left(\dfrac{1}{\left(x-1\right)^2}+\dfrac{-1}{\left(x-1\right)\left(x+1\right)}\right)\)
\(=\dfrac{1}{x-1}-\dfrac{x\left(x-1\right)\left(x+1\right)}{x^2+1}\cdot\left(\dfrac{x+1}{\left(x-1\right)^2\left(x+1\right)}+\dfrac{-1\left(x-1\right)}{\left(x-1\right)\left(x+1\right)\left(x-1\right)}\right)\)
\(=\dfrac{1}{x-1}-\dfrac{x\left(x-1\right)\left(x+1\right)}{x^2+1}\cdot\left(\dfrac{x+1-x+1}{\left(x-1\right)^2\left(x+1\right)}\right)\)
\(=\dfrac{1}{x-1}-\dfrac{x\left(x-1\right)\left(x+1\right)\cdot2}{\left(x^2+1\right)\left(x-1\right)^2\left(x+1\right)}\)
\(=\dfrac{1}{x-1}-\dfrac{2x}{\left(x^2+1\right)\left(x-1\right)}\)
\(=\dfrac{x^2+1}{\left(x-1\right)\left(x^2+1\right)}-\dfrac{2x}{\left(x^2+1\right)\left(x-1\right)}\)
\(=\dfrac{x^2-2x+1}{\left(x-1\right)\left(x^2+1\right)}\)
\(=\dfrac{\left(x-1\right)^2}{\left(x-1\right)\left(x^2+1\right)}\)
\(=\dfrac{x-1}{x^2+1}\)
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