\(\frac{\left[x+2\right]}{x+3}\)   -    \(\frac{x+1}{x-1}\)= ...">
K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

10 tháng 3 2020

\(\frac{x+2}{x+3}-\frac{x+1}{x-1}=\frac{4}{\left(x-1\right)\left(x+3\right)}\left(x\ne-3;x\ne1\right)\)

\(\Leftrightarrow\frac{x+2}{x+3}-\frac{x+1}{x-1}-\frac{4}{\left(x-1\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\frac{\left(x+2\right)\left(x-1\right)}{\left(x+3\right)\left(x-1\right)}-\frac{\left(x+1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}-\frac{4}{\left(x-1\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\frac{x^2+x-2}{\left(x+3\right)\left(x-1\right)}-\frac{x^2+4x+3}{\left(x-1\right)\left(x+3\right)}-\frac{4}{\left(x-1\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\frac{x^2+x-2-x^2-4x-3-4}{\left(x-1\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\frac{-3x-9}{\left(x-1\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\frac{-3\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}=0\)

\(\Leftrightarrow\frac{-3}{x-1}=0\)

=> PT vô nghiệm

10 tháng 3 2020

\(a)\frac{x+2}{x+3}-\frac{5}{x^2+x-6}+\frac{1}{2-x}=\frac{-3}{4}\left(x\ne-3;x\ne2\right)\)

\(\Leftrightarrow\frac{x+2}{x+3}-\frac{5}{\left(x+3\right)\left(x-2\right)}-\frac{1}{x-2}=\frac{-3}{4}\)

\(\Leftrightarrow\frac{x^2-4}{\left(x-2\right)\left(x+3\right)}-\frac{5}{\left(x+3\right)\left(x-2\right)}-\frac{x+3}{\left(x-2\right)\left(x+3\right)}=\frac{-3}{4}\)

\(\Leftrightarrow\frac{x^2-4-5-x-3}{\left(x-2\right)\left(x+3\right)}=\frac{-3}{4}\)

\(\Leftrightarrow\frac{x^2-x-12}{\left(x-2\right)\left(x+3\right)}=\frac{-3}{4}\)

\(\Leftrightarrow\frac{\left(x-4\right)\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}=\frac{-3}{4}\)

\(\Leftrightarrow\frac{x-4}{x-2}=\frac{-3}{4}\)

<=> 4x-16=-3x+6

<=> 4x-16+3x-6=0

<=> 7x-22=0

<=> 7x=22

<=> \(x=\frac{22}{7}\)(TMĐK)
 

10 tháng 3 2020

a,\(\left(3x-2\right)\left(x+6\right)\left(x^2+5\right)=0\)

Ta có: \(x^2+5\ge0\) (vô lí)

\(\Leftrightarrow\orbr{\begin{cases}3x-2=0\\x+6=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{2}{3}\\x=-6\end{cases}}\)

Vậy ....

c, \(4x^2\left(x-1\right)-x+1=0\)

\(\Leftrightarrow4x^3-4x^2-x+1=0\)

\(\Leftrightarrow4x^2\left(x-1\right)-\left(x-1\right)=0\)

\(\Leftrightarrow\left(4x^2-1\right)\left(x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}4x^2-1=0\\x-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}4x^2=1\\x=1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x^2=\frac{1}{4}\\x=1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\pm\frac{1}{2}\\x=1\end{cases}}\)

Vậy ....

10 tháng 3 2020

\(\frac{x+2}{x+3}-\frac{x+1}{x-1}=\frac{4}{\left(x-1\right)\left(x+3\right)}\)

ĐKXĐ: \(x\ne1,x\ne-3\)

PT đã cho \(\Leftrightarrow\frac{\left(x+2\right).\left(x-1\right)-\left(x+1\right).\left(x+3\right)}{\left(x+3\right).\left(x-1\right)}=\frac{4}{\left(x-1\right)\left(x+3\right)}\)

\(\Leftrightarrow\frac{\left(x+2\right).\left(x-1\right)-\left(x+1\right).\left(x+3\right)}{\left(x+3\right).\left(x-1\right)}=\frac{4}{\left(x-1\right)\left(x+3\right)}\)

\(\Rightarrow x^2+x-2-x^2-4x-3=4\Leftrightarrow3x=-1\Leftrightarrow x=\frac{-1}{3}\)

Bài 1: 

a: \(\dfrac{x-1}{x+1}-\dfrac{x+1}{x-1}+\dfrac{4}{\left(x-1\right)\left(x+1\right)}\)

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

\(=\dfrac{-4x+4}{\left(x-1\right)\left(x+1\right)}=\dfrac{-4}{x+1}\)

b: \(=\dfrac{xy\left(x^2+y^2\right)}{x^4y}\cdot\dfrac{1}{x^2+y^2}=\dfrac{x}{x^4}=\dfrac{1}{x^3}\)

c: Đề thiếu rồi bạn

11 tháng 12 2016

a) \(\frac{x-1}{x+1}-\frac{x+1}{x-1}+\frac{4}{x^2-1}\left(ĐK:x\ne\pm1\right)\)

\(=\frac{\left(x-1\right)^2-\left(x+1\right)^2+4}{\left(x-1\right)\left(x+1\right)}\)

\(\frac{x^2-2x+1-x^2-2x-1+4}{\left(x-1\right)\left(x+1\right)}\)

\(=\frac{-4x+4}{\left(x-1\right)\left(x+1\right)}=\frac{-4\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=-\frac{4}{x+1}\)

b) \(\frac{x^3y+xy^3}{x^4y}:\left(x^2+y^2\right)\left(ĐK:x,y\ne0\right)\)

\(=\frac{xy\left(x^2+y^2\right)}{x^4y}\cdot\frac{1}{x^2+y^2}\)

\(=\frac{1}{x^3}\)

11 tháng 2 2017

Cái này là phương trình chứa ẩn ở mẫu đó nha, mình cần sớm

28 tháng 2 2020

\(\Leftrightarrow\frac{5-2x}{3\left(3x-1\right)}+\frac{3\left(x^2-1\right)}{3\left(3x-1\right)}-\frac{\left(x+2\right)\left(1-3x\right)}{3\left(3x-1\right)}=0\)

\(\Rightarrow5-2x+3x^2-3-x+3x^2-2+6x=0\Leftrightarrow6x^2+3x=0\Leftrightarrow3x\left(2x+1\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\x=-\frac{1}{2}\end{matrix}\right.\)

28 tháng 2 2020

\(\Leftrightarrow-\frac{5x-2}{2\left(x-1\right)}+\frac{\left(2x-1\right)\left(x-1\right)}{2\left(x-1\right)}=\frac{1-x-x^2-x+3}{1-x}\Leftrightarrow\frac{2x^2-8x+3}{2\left(x-1\right)}=\frac{x^2+2x-4}{x-1}\)

\(\Rightarrow2x^2-8x+3=2x^2+4x-8\)\(\Leftrightarrow-8x+3=4x-8\Leftrightarrow-12x=-12\Rightarrow x=1\)

26 tháng 2 2022

hic, mk chx học