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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!

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

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

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


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

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

12 tháng 3 2018

bài 1:

b,\(\dfrac{x+2}{x}=\dfrac{x^2+5x+4}{x^2+2x}+\dfrac{x}{x+2}\)(ĐKXĐ:x ≠0,x≠-2)

<=>\(\dfrac{\left(x+2\right)^2}{x\left(x+2\right)}=\dfrac{x^2+5x+4}{x\left(x+2\right)}+\dfrac{x^2}{x\left(x+2\right)}\)

=>\(x^2+4x+4=x^2+5x+4+x^2\)

<=>\(x^2-x^2-x^2+4x-5x+4-4=0\)

<=>\(-x^2-x=0< =>-x\left(x+1\right)=0< =>\left[{}\begin{matrix}x=0\left(loại\right)\\x+1=0< =>x=-1\left(nhận\right)\end{matrix}\right.\)

vậy...............

d,\(\left(x+3\right)^2-25=0< =>\left(x+3-5\right)\left(x+3+5\right)=0< =>\left(x-2\right)\left(x+8\right)=0< =>\left[{}\begin{matrix}x-2=0\\x+8=0\end{matrix}\right.< =>\left[{}\begin{matrix}x=2\\x=-8\end{matrix}\right.\)

vậy............

bài 3:

g,\(\dfrac{4}{x+1}-\dfrac{2}{x-2}=\dfrac{x+3}{x^2-x-2}\)(ĐKXĐ:x khác -1,x khác 2)

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

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

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

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

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

<=>\(x=13\)

vậy..............

mấy ý khác bạn làm tương tụ nhé

chúc bạn học tốt ^ ^

6 tháng 6 2019

a,\(x-\frac{5x+2}{6}=\frac{7-3x}{4}\)

=> \(\frac{12x}{12}-\frac{\left(5x+2\right)2}{12}=\frac{\left(7-3x\right)3}{12}\)

=>\(\frac{12x-10x-4}{12}=\frac{21-9x}{12}\)

=>(khử mẫu)

=>\(12x-10x-4=21-9x\)

=>11x=25

=>x=25/11

b: \(\Leftrightarrow3\left(10x+3\right)=36+4\left(8x+6\right)\)

=>30x+9=36+32x+24

=>32x+60=30x+9

=>2x=-51

=>x=-51/2

c: \(\Leftrightarrow2x-3\left(2x+1\right)=x+6x\)

=>7x=2x-6x-3

=>7x=-4x-3

=>11x=-3

=>x=-3/11

d: \(\Leftrightarrow4\left(x+2\right)-6x=3\left(1-2x+1\right)\)

=>4x+8-6x=3(-2x+2)

=>-2x+8+6x-6=0

=>4x+2=0

=>x=-1/2

16 tháng 1 2019

a)\(x-\dfrac{5x+2}{6}=\dfrac{7-3x}{4}\)

\(\Leftrightarrow\dfrac{12x-10x-4}{12}=\dfrac{21-9x}{12}\)

\(\Leftrightarrow2x-4=21-9x\)

\(\Leftrightarrow2x-4-21+9x=0\)

\(\Leftrightarrow11x-25=0\)

\(\Leftrightarrow x=\dfrac{25}{11}\)

b)\(\dfrac{10x+3}{12}=1+\dfrac{6+8x}{9}\)

\(\Leftrightarrow\dfrac{30x+9}{36}=\dfrac{36+24+32x}{36}\)

\(\Leftrightarrow30x+9=60+32x\)

\(\Leftrightarrow30x+9-60-32x=0\)

\(\Leftrightarrow-2x-51=0\)

\(\Leftrightarrow x=-\dfrac{51}{2}\)

c)\(\dfrac{x}{3}-\dfrac{2x+1}{2}=\dfrac{x}{6}-6\)

\(\Leftrightarrow\dfrac{2x-6x-3}{6}=\dfrac{x-36}{6}\)

\(\Leftrightarrow-4x-3=x-36\)

\(\Leftrightarrow-4x-3-x+36=0\)

\(\Leftrightarrow-5x+33=0\)

\(\Leftrightarrow x=\dfrac{33}{5}\)

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

\(\Leftrightarrow\dfrac{8+4x-6x}{12}=\dfrac{3-6x+3}{12}\)

\(\Leftrightarrow8-2x=6-6x\)

\(\Leftrightarrow8-2x-6+6x=0\)

\(\Leftrightarrow4x+2=0\)

\(\Leftrightarrow x=-\dfrac{1}{2}\)

Tính lại xem đúng không nha haha

16 tháng 1 2019

a) \(x-\dfrac{5x+2}{6}=\dfrac{7-3x}{4}\)

\(\Leftrightarrow\dfrac{24x}{24}-\dfrac{4\left(5x+2\right)}{24}=\dfrac{6\left(7-3x\right)}{24}\)

\(\Leftrightarrow24x-4\left(5x+2\right)=6\left(7-3x\right)\)

\(\Leftrightarrow24x-20x-8=42-18x\)

\(\Leftrightarrow4x-8=42-18x\)

\(\Leftrightarrow4x+18x=42+8\)

\(\Leftrightarrow22x=50\)

\(\Leftrightarrow x=\dfrac{25}{11}\)

Vậy S\(=\left\{\dfrac{25}{11}\right\}\)

27 tháng 6 2018

Mk xin lỗi nha, câu c sai đề

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