\(\dfrac{5}{x-2}\)+\(\dfrac{4}{x-3}\)
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a: =>\(\dfrac{5x-15+4x-8}{\left(x-2\right)\left(x-3\right)}=\dfrac{1}{x}\)

=>\(\dfrac{9x-23}{\left(x-2\right)\left(x-3\right)}=\dfrac{1}{x}\)

=>9x^2-23x=x^2-5x+6

=>8x^2-18x-6=0

=>\(x=\dfrac{9\pm\sqrt{129}}{8}\)

b: =>\(\dfrac{12x+1}{11x-4}=\dfrac{20x+17-20x+8}{18}=\dfrac{25}{18}\)

=>216x+18=275x-100

=>-59x=-118

=>x=2

5 tháng 2 2020

\(\frac{12x+1}{11x-4}+\frac{10x-4}{9}=\frac{20x+17}{18}\left(ĐKXĐ:x\ne\frac{4}{11}\right).\)

\(\Leftrightarrow\frac{18.\left(12x+1\right)}{18.\left(11x-4\right)}+\frac{2.\left(11x-4\right).\left(10x-4\right)}{18.\left(11x-4\right)}=\frac{\left(11x-4\right).\left(20x+17\right)}{18.\left(11x-4\right)}\)

\(\Rightarrow18.\left(12x+1\right)+2.\left(11x-4\right).\left(10x-4\right)=\left(11x-4\right).\left(20x+17\right)\)

\(\Leftrightarrow216x+18+\left(22x-8\right).\left(10x-4\right)=220x^2+187x-80x-68\)

\(\Leftrightarrow216x+18+220x^2-88x-80x+32=220x^2+107x-68\)

\(\Leftrightarrow48x+50+220x^2=220x^2+107x-68\)

\(\Leftrightarrow48x+50+220x^2-220x^2-107x+68=0\)

\(\Leftrightarrow118-59x=0\)

\(\Leftrightarrow59x=118-0\)

\(\Leftrightarrow59x=118\)

\(\Leftrightarrow x=118:59\)

\(\Leftrightarrow x=2\left(TM\right).\)

Vậy phương trình có tập hợp nghiệm là: \(S=\left\{2\right\}.\)

Chúc bạn học tốt!

15 tháng 8 2018

a , \(16x^2+8x+1=\left(4x\right)^2+2.4x.1+1^2=\left(4x+1\right)^2\)

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

15 tháng 8 2018

a,(4x+1)2 e,\(\left(\dfrac{3}{2}x-\dfrac{2}{5}\right)^2\)

b,(x-\(\dfrac{1}{2}\))2 g,\(\left(xy+1\right)^2\)

c,(\(x+\dfrac{3}{2}\))2 h,\(\left(x+5\right)^2\)

d,\(\left(x-\dfrac{5}{4}\right)^2\) i,\(-\left(x-6\right)^2\)

k,\(-\left(2x+3\right)^2\)

a)\(\dfrac{3}{x^2+5x+4}+\dfrac{2}{x^2+10x+24}=\dfrac{4}{3}+\dfrac{9}{x^2+3x-18}\left(đkxđ:x\ne-1;-4;-6;3\right)\)

\(\Leftrightarrow\dfrac{3}{\left(x+1\right)\left(x+4\right)}+\dfrac{2}{\left(x+4\right)\left(x+6\right)}=\dfrac{4}{3}+\dfrac{9}{\left(x+6\right)\left(x-3\right)}\)

\(\Leftrightarrow\dfrac{1}{x+1}-\dfrac{1}{x+4}+\dfrac{1}{x+4}-\dfrac{1}{x+6}=\dfrac{4}{3}+\dfrac{1}{x-3}-\dfrac{1}{x+6}\)

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

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

\(\Leftrightarrow\dfrac{-4}{\left(x+1\right)\left(x-3\right)}=\dfrac{4}{3}\)

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

\(\Leftrightarrow2x-x^2+3=3\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\left(tm\right)\)

b)\(x^2-y^2+2x-4y-10=0\)

\(\Leftrightarrow x^2+2x+1-y^2-4y-4-7=0\)

\(\Leftrightarrow\left(x+1\right)^2-\left(y+2\right)^2=7\)

\(\Leftrightarrow\left(x-y-1\right)\left(x+y+3\right)=7\)

Mà x,yEN*=>x-y-1<x+y+3

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-y-1=1\\x+y+3=7\end{matrix}\right.\\\left\{{}\begin{matrix}x-y-1=-7\\x+y+3=-1\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)

Vậy ...

13 tháng 11 2018

Help me !!!!!

13 tháng 11 2018

Bài 1:

a) \(\dfrac{15xy}{10x^2y}\)

= \(\dfrac{3.5xy}{2.5xyx}\)

= \(\dfrac{3}{2x}\)

d) \(\dfrac{6x\left(x+5\right)^3}{2x^2\left(x+5\right)}\)

= \(\dfrac{3.2x\left(x+5\right)\left(x+5\right)^2}{x.2x\left(x+5\right)}\)

= \(\dfrac{3\left(x+5\right)^2}{x}\)


29 tháng 6 2017

1) \(4x^2+4x+1=\left(2x+1\right)^2\)

2)\(9x^2-24xy+16y^2=\left(3x-4y\right)^2\)

3)\(-x^2+10x-25=-\left(x-5\right)^2\)

4)\(1+12x+36x^2=\left(1+6x\right)^2\)

5) \(\dfrac{x^2}{4}+2xy+4y^2=\left(\dfrac{x}{2}+2y\right)^2\)

6) \(4x^2+4xy+y^2=\left(2x+y\right)^2\)

29 tháng 6 2017

bài toán iêu cầu j z ??? bn

10 tháng 2 2018

d. ĐKXĐ: x khác 1, x khác 3

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

\(\Leftrightarrow\dfrac{\left(x-3\right)\left(x+5\right)}{\left(x-1\right)\left(x-3\right)}=\dfrac{\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x-3\right)}-\dfrac{8}{\left(x-1\right)\left(x-3\right)}\) \(\Leftrightarrow x^2+2x-15=x^2-1-8\)

\(\Leftrightarrow2x-15+1+8=0\)

\(\Leftrightarrow2x-6=0\)

\(\Leftrightarrow x=3\) (loại)

Vậy pt vô nghiệm

27 tháng 6 2018

Mk xin lỗi nha, câu c sai đề

c) (x+6)4 + (x+8)4 = 272

26 tháng 8 2018

a) \(\dfrac{5x-1}{3x+2}=\dfrac{5x-7}{3x-1}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta được:

\(\dfrac{5x-1}{3x+2}=\dfrac{5x-7}{3x-1}\)

\(=\dfrac{5x-1-5x+7}{3x+2-3x+1}\)

\(=\dfrac{-1+7}{2+1}\)

\(=\dfrac{6}{3}\)

\(=2\)

Với \(\dfrac{5x-1}{3x+2}=2\)

\(\Rightarrow5x-1=2\left(3x+2\right)\)

\(\Rightarrow5x-1-2\left(3x+2\right)=0\)

\(\Rightarrow5x-1-6x-4=0\)

\(\Rightarrow-x-5=0\)

\(\Rightarrow x=-5\)

13 tháng 8 2018

giải bất phương trình

a: =>-4x>16

=>x<-4

c: =>20x-25<=21-3x

=>23x<=46

=>x<=2

d: =>20(2x-5)-30(3x-1)<12(3-x)-15(2x-1)

=>40x-100-90x+30<36-12x-30x+15

=>-50x-70<-42x+51

=>-8x<121

=>x>-121/8