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HN
4 tháng 1 2017
\(A=\left(\frac{x}{x^2-25}-\frac{x-5}{x^2+5x}\right):\frac{2x-5}{x^2+5x}+\frac{x+3}{5-x}\)
\(=\left[\frac{x}{\left(x-5\right)\left(x+5\right)}-\frac{x-5}{x\left(x+5\right)}\right]:\frac{2x-5}{x\left(x+5\right)}+\frac{x+3}{5-x}\)
\(=\left[\frac{x^2}{x\left(x-5\right)\left(x+5\right)}-\frac{\left(x-5\right)^2}{x\left(x+5\right)\left(x-5\right)}\right]:\frac{2x-5}{x\left(x+5\right)}+\frac{x+3}{5-x}\)
\(=\left(\frac{x^2-\left(x-5\right)^2}{x\left(x-5\right)\left(x+5\right)}\right).\frac{x\left(x+5\right)}{2x-5}+\frac{x+3}{5-x}\)
\(=\left[\frac{\left(x-x+5\right)\left(x+x-5\right)}{x\left(x-5\right)\left(x+5\right)}\right].\frac{x\left(x+5\right)}{2x-5}+\frac{x+3}{5-x}\)
\(=\frac{5x.\left(2x-5\right)\left(x+5\right)}{x\left(x-5\right)\left(x+5\right)\left(2x-5\right)}+\frac{x+3}{5-x}\)
\(=\frac{5}{x-5}-\frac{x+3}{x-5}\)
\(=\frac{5-x-3}{x-5}\)
\(=\frac{-x+2}{x-5}\)
\(=-\frac{x-2}{x-5}\)
HT
1
15 tháng 6 2018
Quy đồng hết lên đi thì được:
\(x^4-3x^3+2x^2-9x+9=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)\left(x^2+x+3\right)=0\)
JS
26 tháng 2 2020
Sửa đề: x2 + 13x + 41 --> x2 + 13x + 42
Giải:
\(\frac{1}{x^2+3x+2}+\frac{1}{x^2+5x+6}+\frac{1}{x^2+7x+12}+\frac{1}{x^2+9x+20}+\frac{1}{x^2+11x+30}+\frac{1}{x^2+13x+41}=\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}+\frac{1}{\left(x+4\right)\left(x+5\right)}+\frac{1}{\left(x+5\right)\left(x+6\right)}+\frac{1}{\left(x+6\right)\left(x+7\right)}=\frac{1}{2}\)
(ĐKXĐ: \(x\ne\left\{-1;-2;-3;-4;-5;-6;-7\right\}\))
\(\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+2}+\frac{1}{x+2}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+6}+\frac{1}{x+6}-\frac{1}{x+7}=\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{x+1}-\frac{1}{x+7}=\frac{1}{2}\)
\(\Leftrightarrow\frac{x+7-x-1}{\left(x+1\right)\left(x+7\right)}=\frac{1}{2}\)
\(\Leftrightarrow\left(x+1\right)\left(x+7\right)=12\)
\(\Leftrightarrow x^2+8x+7=12\)
⇔x2-8x=5
⇔ x2-8x+(-4)2=5+(-4)2
⇔ x2-8x+16=21
⇔ (x-4)2=21
⇔ x=±21+4
Vậy...
Chúc bạn học tốt@@
11 tháng 2 2019
ĐKXĐ: \(x\ne\left\{-1;-\frac{1}{2}\right\}\)
\(\Leftrightarrow\left(\frac{x^2-4x+1}{x+1}+1\right)+\left(\frac{x^2-5x+1}{2x+1}+1\right)=0\)
\(\Leftrightarrow\frac{x^2-3x+2}{x+1}+\frac{x^2-3x+2}{2x+1}=0\)
\(\Leftrightarrow\left(x^2-3x+2\right)\left(\frac{1}{x+1}+\frac{1}{2x+1}\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right).\frac{3x+2}{\left(x+1\right)\left(2x+1\right)}=0\)
Tập nghiệm: \(S=\left\{1;2;-\frac{2}{3}\right\}\)
15 tháng 12 2018
\(a.ĐKXĐ:\hept{\begin{cases}1-3x\ne0\\3x+1\ne0\\x\ge0\end{cases}\Leftrightarrow\hept{\begin{cases}x=\frac{1}{3}\\...\\x\ge0\end{cases}}}\)
15 tháng 12 2018
\(b,M=\left(\frac{3x}{1-3x}+\frac{2x}{3x+1}\right):\frac{6x^2+10}{1-6x+9x^2}\)
\(=\left(\frac{3x\left(1+3x\right)}{\left(1-3x\right)\left(1+3x\right)}+\frac{2x\left(1-3x\right)}{\left(1-3x\right)\left(1+3x\right)}\right).\frac{\left(1-3x\right)^2}{6x^2+10}\)
\(=\left(\frac{3x+9x^2+2x-6x^2}{\left(1-3x\right)\left(1+3x\right)}\right).\frac{\left(1-3x\right)^2}{6x^2+10}\)
\(=\frac{5x+3x^2}{1+3x}.\frac{1-3x}{2\left(3x^2+5\right)}\)
==>Sai đề không mem
23 tháng 4 2020
a, (3x - 2)(4x + 3) = (2 - 3x)(x - 1)
\(\Leftrightarrow\) (3x - 2)(4x + 3) - (2 - 3x)(x - 1) = 0
\(\Leftrightarrow\) (3x - 2)(4x + 3) + (3x - 2)(x - 1) = 0
\(\Leftrightarrow\) (3x - 2)(4x + 3 + x - 1) = 0
\(\Leftrightarrow\) (3x - 2)(5x + 2) = 0
\(\Leftrightarrow\left[{}\begin{matrix}3x-2=0\\5x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{2}{3}\\x=\frac{-2}{5}\end{matrix}\right.\)
Vậy S = {\(\frac{2}{3}\); \(\frac{-2}{5}\)}
b, x2 + (x + 3)(5x - 7) = 9
\(\Leftrightarrow\) x2 - 9 + (x + 3)(5x - 7) = 0
\(\Leftrightarrow\) (x - 3)(x + 3) + (x + 3)(5x - 7) = 0
\(\Leftrightarrow\) (x + 3)(x - 3 + 5x - 7) = 0
\(\Leftrightarrow\) (x + 3)(6x - 10) = 0
\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\6x-10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=\frac{5}{3}\end{matrix}\right.\)
Vậy S = {-3; \(\frac{5}{3}\)}
c, 2x2 + 5x + 3 = 0
\(\Leftrightarrow\) 2x2 + 2x + 3x + 3 = 0
\(\Leftrightarrow\) 2x(x + 1) + 3(x + 1) = 0
\(\Leftrightarrow\) (x + 1)(2x + 3) = 0
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\2x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\frac{3}{2}\end{matrix}\right.\)
Vậy S = {-1; \(\frac{3}{2}\)}
d, \(\frac{3-2x}{2006}+\frac{3-2x}{2007}+\frac{3-2x}{2008}=\frac{3-2x}{2009}+\frac{3-2x}{2010}\)
\(\Leftrightarrow\) \(\frac{3-2x}{2006}+\frac{3-2x}{2007}+\frac{3-2x}{2008}-\frac{3-2x}{2009}-\frac{3-2x}{2010}=0\)
\(\Leftrightarrow\) (3 - 2x)\(\left(\frac{1}{2006}+\frac{1}{2007}+\frac{1}{2008}-\frac{1}{2009}-\frac{1}{2010}\right)\) = 0
\(\Leftrightarrow\) 3 - 2x = 0
\(\Leftrightarrow\) x = \(\frac{3}{2}\)
Vậy S = {\(\frac{3}{2}\)}
Chúc bn học tốt!!
16 tháng 3 2023
a:=>x^2-1-x=2x-1
=>x^2-x-1=2x-1
=>x^2-3x=0
=>x=0(loại) hoặc x=3(nhận)
b:=>x+2=0 hoặc 5-3x=0
=>x=-2 hoặc x=5/3
c:=>20(1-2x)+6x=9(x-5)-24
=>20-40x+6x=9x-45-24
=>-34x+20=9x-69
=>-43x=-89
=>x=89/43
d: =>x^2+4x+4-x^2-2x+3=2x^2+8x-4x-16-3
=>2x^2+4x-19=-2x+7
=>2x^2+6x-26=0
=>x^2+3x-13=0
=>\(x=\dfrac{-3\pm\sqrt{61}}{2}\)
e: =>(2x-3)(2x-3-x-1)=0
=>(2x-3)(x-4)=0
=>x=4 hoặc x=3/2
Đặt \(2x^2-1=a\)
\(\Rightarrow\frac{a}{x}+\frac{5x}{a-x}=-7\)
\(\Leftrightarrow2x^2-6ax-a^2=0\)
Đặt \(a=tx\)
\(\Rightarrow2x^2-6tx^2-t^2x^2=0\)
\(\Leftrightarrow2-6t-t^2=0\)
Làm nốt nha