BT
1
K
Khách
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21 tháng 12 2021
\(=\dfrac{1}{x+1}-\dfrac{8}{\left(x+1\right)\left(x-4\right)}=\dfrac{x-4-8}{\left(x+1\right)\left(x-4\right)}=\dfrac{x-12}{\left(x+1\right)\left(x-4\right)}=\dfrac{-11}{2\cdot\left(-3\right)}=\dfrac{11}{6}\)
17 tháng 11 2023
\(\dfrac{1}{x-3}-\dfrac{1}{x}=\dfrac{x-\left(x-3\right)}{x\left(x-3\right)}=\dfrac{x-x+3}{x\left(x-3\right)}=\dfrac{3}{x\left(x-3\right)}\)
\(B=\dfrac{1}{x^2-3x}+\dfrac{1}{x^2-9x+18}+\dfrac{1}{x^2-15x+54}+\dfrac{1}{x^2-21x+108}\)
\(=\dfrac{1}{x\left(x-3\right)}+\dfrac{1}{\left(x-3\right)\left(x-6\right)}+\dfrac{1}{\left(x-6\right)\left(x-9\right)}+\dfrac{1}{\left(x-9\right)\left(x-12\right)}\)
\(=\dfrac{1}{3}\left(\dfrac{3}{x\left(x-3\right)}+\dfrac{3}{\left(x-3\right)\left(x-6\right)}+\dfrac{3}{\left(x-6\right)\left(x-9\right)}+\dfrac{3}{\left(x-9\right)\left(x-12\right)}\right)\)
\(=\dfrac{1}{3}\left(-\dfrac{1}{x}+\dfrac{1}{x-3}-\dfrac{1}{x-3}+\dfrac{1}{x-6}-\dfrac{1}{x-6}+\dfrac{1}{x-9}-\dfrac{1}{x-9}+\dfrac{1}{x-12}\right)\)
\(=\dfrac{1}{3}\left(-\dfrac{1}{x}+\dfrac{1}{x-12}\right)\)
\(=\dfrac{1}{3}\cdot\dfrac{-\left(x-12\right)+x}{x\left(x-12\right)}\)
\(=\dfrac{4}{x\left(x-12\right)}\)
KC
2
26 tháng 3 2022
đk : x khác 0 ; 1 ; 2
\(2\left(x-1\right)\left(x-2\right)-x\left(x-2\right)=2x\left(x-1\right)\)
\(\Leftrightarrow2\left(x^2-3x+2\right)-x^2+2x=2x^2-2x\)
\(\Leftrightarrow-6x+4-x^2+2x=-2x\Leftrightarrow x^2+2x-4=0\)
\(\Leftrightarrow\left(x+1\right)^2-5=0\Leftrightarrow\left[{}\begin{matrix}x=-1-\sqrt{5}\\x=-1+\sqrt{5}\end{matrix}\right.\left(tm\right)\)
26 tháng 3 2022
Thấy hơi lạ lạ, mấy bạn coi rồi nói cho mình nha! Cảm ơn~
3 tháng 12 2022
a: \(=\dfrac{4xy+x^2-2xy+y^2}{2\left(x+y\right)\left(x-y\right)}\cdot\dfrac{2x}{x+y}-\dfrac{y}{x-y}\)
\(=\dfrac{x}{x-y}-\dfrac{y}{x-y}=1\)
b: \(=\dfrac{x^2+x-2-2x^2-2x}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{3\left(x+1\right)}{x}+\dfrac{4x^2+x+7}{x\left(x-1\right)}\)
\(=\dfrac{-x^2-x-2}{\left(x-1\right)}\cdot\dfrac{3}{x}+\dfrac{4x^2+x+7}{x\left(x-1\right)}\)
\(=\dfrac{4x^2+x+7-3x^2-3x-6}{x\left(x-1\right)}=\dfrac{x^2-2x+1}{x\left(x-1\right)}=\dfrac{x-1}{x}\)
c: \(=\dfrac{1}{x+4}-\dfrac{1}{x+5}+\dfrac{1}{x+5}-\dfrac{1}{x+6}+\dfrac{1}{x+6}-\dfrac{1}{x+7}\)
\(=\dfrac{x+7-x-4}{\left(x+7\right)\left(x+4\right)}=\dfrac{3}{\left(x+4\right)\left(x+7\right)}\)
N
1
\(\dfrac{1}{x+1}-\dfrac{1}{x}\) MTC: \(x\left(x+1\right)\)
\(=\dfrac{x}{x\left(x+1\right)}-\dfrac{x+1}{x\left(x+1\right)}\)
\(=\dfrac{x-\left(x+1\right)}{x\left(x+1\right)}\)
\(=\dfrac{x-x-1}{x\left(x+1\right)}\)
\(=\dfrac{-1}{x\left(x+1\right)}\)