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10 tháng 8 2018

\(\dfrac{12}{8+x^3}=1+\dfrac{1}{x+2}\) ( ĐK : \(x\ne-2\) )

\(\Leftrightarrow\dfrac{12}{x^3+2^3}=1+\dfrac{1}{x+2}\)

\(\Leftrightarrow\dfrac{12}{\left(x+2\right)\left(x^2-2x+4\right)}=\dfrac{\left(x+2\right)\left(x^2-2x+4\right)}{\left(x+2\right)\left(x^2-2x+4\right)}+\dfrac{x^2-2x+4}{\left(x+2\right)\left(x^2-2x+4\right)}\)

\(\Leftrightarrow12=\left(x+2\right)\left(x^2-2x+4\right)+x^2-2x+4\)

\(\Leftrightarrow x^3+8+x^2-2x+4=12\)

\(\Leftrightarrow x^3+x^2-2x=0\)

\(\Leftrightarrow x\left(x^2+x-2\right)=0\)

\(\Leftrightarrow x\left(x-1\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(N\right)\\x=1\left(N\right)\\x=-2\left(L\right)\end{matrix}\right.\)

Vậy \(S=\left\{0;1\right\}\)

10 tháng 8 2018

Thank you ! <3 !! :))

6 tháng 1 2022

⇔ \(\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+5\right)}+\dfrac{1}{\left(x+5\right)\left(x+6\right)}=\dfrac{1}{8}\)

⇔ \(\dfrac{1}{x+2}-\dfrac{1}{x+3}+\dfrac{1}{x+3}-\dfrac{1}{x+4}+\dfrac{1}{x+4}-\dfrac{1}{x+5}+\dfrac{1}{x+5}-\dfrac{1}{x+6}=\dfrac{1}{8}\)

⇔ \(\dfrac{1}{x+2}-\dfrac{1}{x+6}=\dfrac{1}{8}\)

⇔ \(\dfrac{x+6-x-2}{\left(x+2\right)\left(x+6\right)}=\dfrac{1}{8}\)

⇔ \(\dfrac{4}{x^2+8x+12}=\dfrac{1}{8}\)

⇔ \(x^2+8x+12=32\)

⇔ \(x^2+8x-20=0\)

⇔ \(\left(x-2\right)\left(x+10\right)=0\)

⇔ \(\left[{}\begin{matrix}x=2\\x=-10\end{matrix}\right.\)

6 tháng 1 2022

Sửa lại đề nha:

 \(\dfrac{1}{x^2+9x+12}thành\dfrac{1}{x^2+9x+20}\)

20 tháng 3 2017

Ta có : 1+\(\dfrac{1}{x+2}\) = \(\dfrac{12}{8-x^3}\) (đkxđ x\(\ne\pm2\) )

\(\Leftrightarrow\) \(\dfrac{1}{x+2}\) = \(\dfrac{12}{8-x^3}-1\)

\(\Leftrightarrow\)\(\dfrac{1}{x+2}=\dfrac{12-\left(8-x^3\right)}{8-x^3}\)

\(\Leftrightarrow\dfrac{1}{x+2}=\dfrac{x^3+4}{8-x^3}\)

\(\Leftrightarrow8-x^3=\left(x+2\right)\left(x^3+4\right)\)

\(\Leftrightarrow8-x^3=x^4+4x+2x^3+8\)

\(\Leftrightarrow-x^3-x^4-4x-2x^3=8-8\)

\(\Leftrightarrow-x^4-3x^3-4x=0\)

\(\Leftrightarrow-x\left(x^3+3x^2+4\right)=0\)

\(\Rightarrow-x=0\)\(\Rightarrow x=0\) (TM x\(\ne\pm2\))

22 tháng 1 2018

ĐKXĐ

x≠3 ; x≠-3

22 tháng 1 2018

ĐKXĐ x≠3 ; x≠-3

\(\dfrac{2x-1}{x+3}=\dfrac{2x+1}{x-3}\)

=> (2x-1)(x-3)=(2x+1)(x+3)

⇔2x2-6x-x+3=2x2+6x+x+3

⇔2x2-2x2-7x-6x=3-3

⇔ -13x=0

⇔x=0 (tm)

vậy phương trình trên có tập no S={0}

a) ĐKXĐ: \(x\notin\left\{2;-2\right\}\)

Ta có: \(\dfrac{x+1}{x-2}-\dfrac{5}{x+2}=\dfrac{12}{x^2-4}+1\)

\(\Leftrightarrow\dfrac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\dfrac{5\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}=\dfrac{12}{\left(x-2\right)\left(x+2\right)}+\dfrac{x^2-4}{\left(x-2\right)\left(x+2\right)}\)

Suy ra: \(x^2+3x+2-5x+10=12+x^2-4\)

\(\Leftrightarrow x^2-2x+12-8-x^2=0\)

\(\Leftrightarrow-2x+4=0\)

\(\Leftrightarrow-2x=-4\)

hay x=2(loại)

Vậy: \(S=\varnothing\)

b) Ta có: \(\left|2x+6\right|-x=3\)

\(\Leftrightarrow\left|2x+6\right|=x+3\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+6=x+3\left(x\ge-3\right)\\-2x-6=x+3\left(x< -3\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-x=3-6\\-2x-x=3+6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\left(nhận\right)\\x=-3\left(loại\right)\end{matrix}\right.\)

Vậy: S={-3}

23 tháng 4 2017

Pt trên có MSC là \(\left(x-1\right)\left(x^2+x+1\right)\)

Quy đồng mẫu số :

\(\dfrac{1}{x-1}+\dfrac{7x-10}{x^3-1}-\dfrac{3}{x^2+x+1}=0\)

( ĐKXĐ \(x\ne1\))

\(\Leftrightarrow\dfrac{x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{7x-10}{x^3-1}-\dfrac{3x-3}{\left(x-1\right)\left(x^2+x+1\right)}=0\)

\(\Leftrightarrow\dfrac{x^2+x+1+7x-10-3x+3}{\left(x-1\right)\left(x^2+x+1\right)}=0\)

\(\Leftrightarrow\) \(\dfrac{x^2+5x-6}{\left(x-1\right)\left(x^2+x+1\right)}=0\)

\(\Leftrightarrow x^2+5x-6=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+6\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=1\left(KTMĐK\right)\\x=-6\left(TMĐK\right)\end{matrix}\right.\)

Vậy \(S=\left\{-6\right\}\)

23 tháng 4 2017

ĐKXĐ: \(x\ne1\); \(x\ne-1\)

\(\dfrac{1}{x-1}+\dfrac{7x-10}{x^3-1}-\dfrac{3}{x^2+x+1}=0\)

\(\Leftrightarrow\dfrac{x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{7x-10}{\left(x-1\right)\left(x^2+x+1\right)}-\dfrac{3\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=0\)

\(\Rightarrow x^2+x+1+7x-10-3x+3=0\)

\(\Leftrightarrow x^2+5x-6=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+6\right)=0\)

\(\Leftrightarrow x-1=0\) ; \(x+6=0\)

+) \(x-1=0\)

\(\Leftrightarrow x=1\) (Không thỏa mãn ĐKXĐ)

+) \(x+6=0\)

\(\Leftrightarrow x=-6\) (Thỏa mãn ĐKXĐ)

Tập nghiệm: \(S=\left\{-6\right\}\)

13 tháng 3 2017

với x>0 thì pt luôn xác định.

\(\Rightarrow\dfrac{x^3+8}{x^3+8}+\dfrac{x^2-2x+4}{x^3+8}=\dfrac{12}{x^3+8}\)

\(\Leftrightarrow x^3+8+x^2-2x+4=12\)

\(\Leftrightarrow x^3+x^2-2x=0\)

\(x\left(x^2+x-2\right)=0\Rightarrow x=0\) hoặc \(x^2+x-2=0\)

x=0 hoac (x\(^2\)-1) +(x-1) =0

x=0 hoặc (x-1)(x+2)=0

x=0 hoax x=1 hoặc x=2 vỉ x>0 nên pt có 2 nghiệm là x=1 , x=2.

12 tháng 3 2017

x = 0

\(\Leftrightarrow x^2-x-x-1=-1\)

=>x(x-2)=0

=>x=2

15 tháng 1 2022

ĐKXĐ:\(\left\{{}\begin{matrix}x\ne-1\\x\ne0\end{matrix}\right.\)

\(\dfrac{x-1}{x+1}-\dfrac{1}{x}=\dfrac{-1}{x\left(x+1\right)}\\ \Leftrightarrow\dfrac{x\left(x-1\right)}{x\left(x+1\right)}-\dfrac{\left(x+1\right)}{x\left(x+1\right)}=\dfrac{-1}{x\left(x+1\right)}\\ \Leftrightarrow\dfrac{x^2-x-x-1}{x\left(x+1\right)}=\dfrac{-1}{x\left(x+1\right)}\\ \Leftrightarrow x^2-2x-1=-1\\ \Leftrightarrow x^2-2x=0\\ \Leftrightarrow x\left(x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=2\left(tm\right)\end{matrix}\right.\)

 

1 tháng 5 2018

a) \(\dfrac{\left(x+1\right)^2}{x^2-1}-\dfrac{\left(x-1\right)^2}{x^2-1}=\dfrac{16}{x^2-1}\)

=>\(\left(x+1\right)^2-\left(x-1\right)^2=16\)

=>\(x^2+2x+1-x^2+2x-1=16\)

=>4x=16=>x=4

b)\(\dfrac{12}{x^2-4}-\dfrac{x+1}{x-2}+\dfrac{x+7}{x+2}=0\)

=>\(\dfrac{12}{x^2-4}-\dfrac{\left(x+1\right)\left(x+2\right)}{x^2-4}+\dfrac{\left(x+7\right)\left(x-2\right)}{x^2-4}=0\)

=>\(12-\left(x+1\right)\left(x+2\right)+\left(x+7\right)\left(x-2\right)=0\)

=>\(12-x^2-3x-2+x^2+5x-14=0\)

=>2x-4=0=>2x=4=>x=2

c)\(\dfrac{12}{8+x^3}=1+\dfrac{1}{x+2}\)

=>\(\dfrac{12}{8+x^3}=\dfrac{x^3+8}{x^3+8}+\dfrac{x^2-2x+4}{x^3+8}\)

=>\(12=x^3+8+x^2-2x+4\)

=>\(x^3+x^2-2x=0\)

=>\(x^3-x+x^2-x=0\)

1 tháng 5 2018

c)=>\(x\left(x^2-1\right)+x\left(x-1\right)=0\)

=>\(x\left(x-1\right)\left(x+1\right)+x\left(x-1\right)=0\)

=>\(x\left(x-1\right)\left(x+2\right)=0\)

=>x=?