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a) Ta có: \(\hept{\begin{cases}\left(2x+3\right)⋮\left(x-5\right)\\\left(x-5\right)⋮\left(x-5\right)\end{cases}}\Rightarrow\hept{\begin{cases}\left(2x+3\right)⋮\left(x-5\right)\\2\left(x-5\right)=\left(2x-10\right)⋮\left(x-5\right)\end{cases}}\)
=> \(\left(2x+3\right)-\left(2x-10\right)⋮\left(x-5\right)\)
\(\Leftrightarrow13⋮\left(x-5\right)\)
\(\Rightarrow x-5\inƯ\left(13\right)=\left\{\pm1;\pm13\right\}\)
\(\Rightarrow x\in\left\{-8;4;6;18\right\}\)
b) Ta có: \(\hept{\begin{cases}\left(3x-2\right)⋮\left(2x+3\right)\\\left(2x+3\right)⋮\left(2x+3\right)\end{cases}\Rightarrow}\hept{\begin{cases}2\left(3x-2\right)=\left(6x-4\right)⋮\left(2x+3\right)\\3\left(2x+3\right)=\left(6x+9\right)⋮\left(2x+3\right)\end{cases}}\)
=> \(6x+9-6x+4⋮\left(2x+3\right)\)
\(\Rightarrow13⋮\left(2x+3\right)\)
\(\Rightarrow2x+3\inƯ\left(13\right)=\left\{\pm1;\pm13\right\}\)
\(\Rightarrow2x\in\left\{-16;-4;-2;10\right\}\)
\(\Rightarrow x\in\left\{-8;-2;-1;5\right\}\)
a)
2.(x-3)-3.(x-5)=4.(3-x)-18
<=>2x-6-3x+15 =12-4x-18
<=>9-x =-4x-6
<=>9-x+4x+6 =0
<=>3x+15 =0
<=>3x =-15
<=>x =-5
a: =>2x-6-3x+10=12-4x-18
=>-x+4=-4x-6
=>3x=-10
=>x=-10/3
b: =>6x+33 chia hết cho 3x+2
=>6x+4+29 chia hết cho 3x+2
=>\(3x+2\in\left\{1;-1;29;-29\right\}\)
=>\(x\in\left\{-\dfrac{1}{3};-1;9;-\dfrac{31}{3}\right\}\)
a)\(\frac{x+11}{x-6}=\frac{x-6+17}{x-6}=\frac{x-6}{x-6}+\frac{17}{x-6}\)
=>x-6\(\in\) Ư(17)
x-6 | 1 | -1 | 17 | -17 |
x | 7 | 5 | 23 | -11 |
\(^{X^2-3X-5⋮X-3}\)
\(\Leftrightarrow X\left(X-3\right)-5⋮X-3\)
\(Do\left(x-3\right)⋮x-3\Rightarrow x\left(x-3\right)⋮x-3\Rightarrow5⋮x-3\)
\(\Rightarrow x-3\inư\left(5\right)=-1,1-5,5\)
\(\Rightarrow x=2,4,-2,8\)
ko thấy rõ