(x^2+2x+2)/(x+1) + (x^2+8x+20)/(x+4) = (x^2+4x+6)/(x+2) + (x^2+6x+12)/(x+3)
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C
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VT
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NC
4 tháng 3 2021
\(\frac{x^2-2x+2}{x-1}+\frac{x^2-8x+20}{x-4}=\frac{x^2-4x+6}{x-2}+\frac{x^2-6x+12}{x-3}\)\(ĐKXĐ:x\ne1;2;3;4\)
\(\Leftrightarrow\frac{\left(x-1\right)^2+1}{x-1}+\frac{\left(x-4\right)^2+4}{x-4}=\frac{\left(x-2\right)^2+2}{x-2}+\frac{\left(x-3\right)^2+3}{x-3}\)
\(\Leftrightarrow\left(\frac{\left(x-1\right)^2}{x-1}+\frac{1}{x-1}\right)+\left(\frac{\left(x-4\right)^2}{x-4}+\frac{4}{x-4}\right)=\left(\frac{\left(x-2\right)^2}{x-2}+\frac{2}{x-2}\right)+\left(\frac{\left(x-3\right)^2}{x-3}+\frac{3}{x-3}\right)\)
\(\Leftrightarrow x-1+\frac{1}{x-1}+x-4+\frac{1}{x-4}=x-2+\frac{1}{x-2}+x-3+\frac{1}{x-3}\)
\(\Leftrightarrow\frac{1}{x-1}+\frac{4}{x-4}=\frac{2}{x-2}+\frac{3}{x-3}\)
\(\Leftrightarrow\frac{x-4+4x-4}{\left(x-1\right)\left(x-4\right)}=\frac{2x-6+3x-6}{\left(x-2\right)\left(x-3\right)}\)
\(\Leftrightarrow\frac{5x-8}{x^2-5x+4}=\frac{5x-12}{x^2-5x+6}\)
\(\Leftrightarrow\left(5x-8\right)\left(x^2-5x+6\right)=\left(5x-12\right)\left(x^2-5x+4\right)\)
Tự giải ra rồi tìm x nhé
13 tháng 3 2022
dấu suy ra số 4 là 1/(x+1) + 1/(x+4) mà.
N
1
30 tháng 6 2022
\(\Leftrightarrow\dfrac{x^2+2x+1-1}{x+1}+\dfrac{x^2+8x+16+4}{x+4}=\dfrac{x^2+4x+4+2}{x+2}+\dfrac{x^2+6x+9+3}{x+3}\)
\(\Leftrightarrow x+1-\dfrac{1}{x+1}+x+4+\dfrac{4}{x+4}=x+2+\dfrac{2}{x+2}+x+3+\dfrac{3}{x+3}\)
\(\Leftrightarrow2x+5-\dfrac{1}{x+1}+\dfrac{4}{x+4}=2x+5+\dfrac{2}{x+2}+\dfrac{3}{x+3}\)
=>-x-4+4x+4=2x+6+3x+6
=>3x=5x+12
=>-2x=12
hay x=-6(nhận)
KN
24 tháng 2 2018
\(\dfrac{x^2+2x+2}{x+1}+\dfrac{x^2+8x+20}{x+4}=\dfrac{x^2+4x+6}{x+2}+\dfrac{x^2+6x+12}{x+3}\)\(\Leftrightarrow\)\(\dfrac{x^2+2x+1+1}{x+1}+\dfrac{x^2+8x+16+4}{x+4}=\dfrac{x^2+4x+4+2}{x+2}+\dfrac{x^2+6x+9+3}{x+3}\)
\(\Leftrightarrow\) \(\dfrac{\left(x+1\right)^2+1}{x+1}+\dfrac{\left(x+4\right)^2+4}{x+4}=\dfrac{\left(x+2\right)^2+2}{x+2}+\dfrac{\left(x+3\right)^2+3}{x+3}\)
\(\Leftrightarrow\) \(x+1+\dfrac{1}{x+1}+x+4+\dfrac{4}{x+4}=x+2+\dfrac{2}{x+2}+x+3+\dfrac{3}{x+3}\)
\(\Leftrightarrow\) \(\dfrac{1}{x+1}\) + \(\dfrac{4}{x+4}\) - \(\dfrac{2}{x+2}\) - \(\dfrac{3}{x+3}\) = x + 2 + x + 3 - x - 1 - x - 4
\(\Leftrightarrow\) \(\dfrac{1}{x+1}\) + \(\dfrac{4}{x+4}\) - \(\dfrac{2}{x+2}\) - \(\dfrac{3}{x+3}\) = 0
\(\Leftrightarrow\) \(\dfrac{1}{x+1}\) + \(\dfrac{4}{x+4}\) = \(\dfrac{2}{x+2}\) + \(\dfrac{3}{x+3}\)
\(\Leftrightarrow\) \(\dfrac{x+4}{\left(x+1\right)\left(x+4\right)}\) + \(\dfrac{4\left(x+1\right)}{\left(x+1\right)\left(x+4\right)}\) = \(\dfrac{2\left(x+3\right)}{\left(x+3\right)\left(x+2\right)}\) + \(\dfrac{3\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}\)
\(\Leftrightarrow\) \(\dfrac{x+4+4x+4}{x^2+5x+4}\) = \(\dfrac{2x+6+3x+6}{x^2+5x+6}\)
\(\Leftrightarrow\) \(\dfrac{5x+8}{x^2+5x+4}\) = \(\dfrac{5x+12}{x^2+5x+6}\)
Đặt 5x + 8 = y; x2 + 5x + 4 = t, ta có:
\(\dfrac{y}{t}\) = \(\dfrac{y+4}{t+2}\)
\(\Leftrightarrow\) \(\dfrac{y\left(t+2\right)}{t\left(t+2\right)}\) = \(\dfrac{t\left(y+4\right)}{t\left(t+2\right)}\)
\(\Leftrightarrow\) yt + 2y = yt + 4t
\(\Leftrightarrow\) 2y = 4t
\(\Leftrightarrow\) 2(5x + 8) = 4(x2 + 5x + 4)
\(\Leftrightarrow\) 10x + 16 = 4x2 + 20x + 16
\(\Leftrightarrow\) 16 - 16 = 4x2 + 20x - 10x
\(\Leftrightarrow\) 0 = 4x2 + 10x
\(\Leftrightarrow\) 2x(2x + 5) = 0
\(\Leftrightarrow\)\(\left\{{}\begin{matrix}x=0\\2x+5=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\x=-\dfrac{5}{2}\end{matrix}\right.\)
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