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1 tháng 8 2023

\(\dfrac{x+1}{x+2}:\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\)

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

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

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

29 tháng 6 2021

4 câu đầu hìn như sai đề :v

`m)(3/2-2/(-5)):x-1/2=3/2`

`<=>(3/2+2/5):x=3/2+1/2=2`

`<=>19/10:x=2`

`<=>x=19/10:2=19/20`

`n)(3/2-5/11-3/13)(2x-2)=(-3/4+5/22+3/26)`

`<=>(3/2-5/11-3/13)(2x-2)+3/4-5/22-3/26=0`

`<=>(3/2-5/11-3/13)(2x-2)+1/2(3/2-5/11-3/13)=0`

`<=>(3/2-5/11-3/13)(2x-2+1/2)=0`

Mà `3/2-5/11-3/13>0`

`<=>2x-2+1/2=0`

`<=>2x-3/2=0`

`<=>2x=3/2<=>x=3/4`

29 tháng 6 2021

Câu i không có dấu "=" sao tìm x :v

24 tháng 7 2017

câu d

\(D=\dfrac{\left(1-x^2\right)}{x}\left(\dfrac{x^2}{x+3}-1\right)+\dfrac{3x^2-14x+3}{x^2+3x}\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\left\{-3;0\right\}\\D=\dfrac{\left(1-x^2\right)\left(x^2-x-3\right)+3x^2-14x+3}{x\left(x+3\right)}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\left\{-3;0\right\}\\D=\dfrac{x^2-x-3-x^4+x^3-3x^2+3x^2-14x+3}{x\left(x+3\right)}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\left\{-3;0\right\}\\D=\dfrac{-x^4+x^3+x^2-15x}{x\left(x+3\right)}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\left\{-3;0\right\}\\D=\dfrac{-x\left(x^3-x^2-x+15\right)}{x\left(x+3\right)}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\left\{-3;0\right\}\\D=\dfrac{-\left(x^3-x^2-x+15\right)}{\left(x+3\right)}\end{matrix}\right.\)

29 tháng 6 2021

`h)x/2-1/x=1/12(x ne 0)`

`<=>6x^2-12=x`

`<=>6x^2-x-12=0`

`<=>6x^2-9x+8x-12=0`

`<=>3x(2x-3)+4(2x-3)=0`

`<=>(2x-3)(3x+4)=0`

`<=>` \(\left[ \begin{array}{l}x=\dfrac32\\x=-\dfrac43\end{array} \right.\) 

`i)x^2-7/6x+1/3=0`

`<=>6x^2-7x+2=0`

`<=>6x^2-3x-4x+2=0`

`<=>3x(2x-1)-2(2x-1)=0`

`<=>(2x-1)(3x-2)=0`

`<=>` \(\left[ \begin{array}{l}x=\dfrac12\\x=\dfrac23\end{array} \right.\) 

Câu cuối không có dấu "=" nên không tìm được x :v

29 tháng 6 2021

- Hai câu h, i bấm nốt đáp án để đẹp nha ;-; câu k thiếu đề :v

28 tháng 11 2022

a: \(=\dfrac{4a^2-4a+1-4a^2-2a+6a+3}{\left(2a-1\right)\left(2a+1\right)}\)

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

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

d: \(=\dfrac{x-5+6x}{x\left(x+3\right)}=\dfrac{7x-5}{x\left(x+3\right)}\)

e: \(=\dfrac{x^2-4+3}{x-2}=\dfrac{x^2-1}{x-2}\)

i: \(=\dfrac{x}{x\left(x-4\right)}-\dfrac{3}{5x}=\dfrac{1}{x-4}-\dfrac{3}{5x}\)

\(=\dfrac{5x-3x+12}{5x\left(x-4\right)}=\dfrac{2x+12}{5x\left(x-4\right)}\)

1: Sửa đề: 2/x+2

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

=>\(\dfrac{2x+1+2x-4}{x^2-4}=\dfrac{-3\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)

=>4x-3=-3x-6

=>7x=-3

=>x=-3/7(nhận)

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

=>9x-3x^2+3-x+3-9x+x-3x^2=2(3x-1)(x-3)

=>-6x^2+6=2(3x^2-10x+3)

=>-6x^2+6=6x^2-20x+6

=>-12x^2+20x=0

=>-4x(3x-5)=0

=>x=5/3(nhận) hoặc x=0(nhận)

3: \(\Leftrightarrow x\cdot\dfrac{8}{3}-\dfrac{2}{3}=1+\dfrac{5}{4}-\dfrac{1}{2}x\)

=>x*19/6=35/12

=>x=35/38

Giải các phương trình có chứa ẩn ở mẫu sau: a, \(\dfrac{x-3}{x-2}+\dfrac{x+2}{x}=2\) b, \(\left(x-2\right)\left(\dfrac{2}{3}x-6\right)=0\) d, \(\dfrac{x}{x+1}-\dfrac{2x-3}{x-1}=\dfrac{2x+3}{x^2-1}\) f, \(\dfrac{x-1}{x}+\dfrac{x-2}{x+1}=2\) g, \(\dfrac{x}{x-1}+\dfrac{x-1}{x}=2\) h, \(\dfrac{x+3}{x+1}+\dfrac{x-2}{x}=2\) i, \(\dfrac{2}{x+1}-\dfrac{3}{x-1}=5\) j, \(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}=\dfrac{8}{4x^2-1}\) k, \(\dfrac{3x-1}{x-1}-\dfrac{2x+5}{x-3}=1\) l,...
Đọc tiếp

Giải các phương trình có chứa ẩn ở mẫu sau:

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

b, \(\left(x-2\right)\left(\dfrac{2}{3}x-6\right)=0\)

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

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

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

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

i, \(\dfrac{2}{x+1}-\dfrac{3}{x-1}=5\)

j, \(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}=\dfrac{8}{4x^2-1}\)

k, \(\dfrac{3x-1}{x-1}-\dfrac{2x+5}{x-3}=1\)

l, \(\dfrac{2}{x+1}-\dfrac{1}{xx-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

m, \(\dfrac{3x-1}{x-1}-\dfrac{2x+5}{x+3}+\dfrac{4}{x^2+2x-3}=1\)

n, \(\dfrac{x+2}{x-2}-\dfrac{1}{x}=\dfrac{2}{x\left(x-2\right)}\)

o, \(\dfrac{x-2}{x+2}+\dfrac{3}{x-2}=\dfrac{x^2-11}{x^2-4}\)

p, \(\dfrac{x+4}{x+1}+\dfrac{x}{x-1}=\dfrac{2x^2}{x^2-1}\)

z, \(\dfrac{2x}{x-1}+\dfrac{4}{x^2+2x-3}=\dfrac{2x-5}{x+3}\)

q, \(\dfrac{x^2-x}{x+3}-\dfrac{x^2}{x-3}=\dfrac{7x^2-3x}{9-x^2}\)

r, \(\dfrac{1}{x-3}+2=\dfrac{5}{x-1}+x\)

s, \(\dfrac{2}{x^2+4x-21}=\dfrac{3}{x-3}\)

3
30 tháng 4 2018

4)a)\(\dfrac{x+5}{x-5}-\dfrac{x-5}{x+5}=\dfrac{20}{x^2-25}\)(1)

ĐKXĐ:\(\left\{{}\begin{matrix}x-5\ne0\\x+5\ne0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ne5\\x\ne-5\end{matrix}\right.\)

(1)\(\Rightarrow\left(x+5\right)\left(x+5\right)-\left(x-5\right)\left(x-5\right)=20\)

\(\Leftrightarrow x^2+10x+25-\left(x^2-10x+25\right)=20\)

\(\Leftrightarrow x^2+10x+25-x^2+10x-25=20\)

\(\Leftrightarrow x^2-x^2+10x+10x=-25+25=20\)

\(\Leftrightarrow20x=20\)

\(\Leftrightarrow x=1\left(nh\text{ậ}n\right)\)

S=\(\left\{1\right\}\)

30 tháng 4 2018

mấy bài còn lại dễ ẹt cứ bình tĩnh làm là ok

1: \(\Leftrightarrow\left(x+2\right)\left(x-2\right)+3\left(x+1\right)=3+x^2-x-2\)

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

=>-4x=-2

hay x=1/2

2: \(\Leftrightarrow\left(x+6\right)^2+\left(x-5\right)^2=2x^2+23x+61\)

\(\Leftrightarrow x^2+12x+36+x^2-10x+25=2x^2+23x+61\)

\(\Leftrightarrow2x^2+23x+61=2x^2+2x+11\)

=>21x=-50

hay x=-50/21

3: \(\Leftrightarrow6\left(x-8\right)+\left(x+2\right)\left(x-5\right)=-18-\left(x-5\right)\left(x-8\right)\)

\(\Leftrightarrow6x-48+x^2-3x-10+18+x^2-13x+40=0\)

\(\Leftrightarrow2x^2-10x=0\)

=>2x(x-5)=0

=>x=0(nhận) hoặc x=5(loại)