\(\Leftrightarrow\frac{108-x}{92}+1+\frac{107-x}{93}+1+\frac{106-x}{94}+1+\frac{105-x}{95}=0.\)

\(\Leftrightarrow\frac{108+92-x}{92}+\frac{107+93-x}{93}+\frac{106+94-x}{94}+\frac{105+95-x}{95}=0\)

\(\Leftrightarrow\frac{200-x}{92}+\frac{200-x}{93}+\frac{200-x}{94}+\frac{200-x}{95}=0\)

\(\Leftrightarrow\left(200-x\right)\left(\frac{1}{92}+\frac{1}{93}+\frac{1}{94}+\frac{1}{95}\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}200-x=0\Leftrightarrow x=200\\\frac{1}{92}+\frac{1}{93}+\frac{1}{94}+\frac{1}{95}\ne0\end{cases}}\)

Vậy nghiệm của phương trình là 200

Ta có : 

\(\frac{108-x}{92}+\frac{107-x}{93}+\frac{106-x}{94}+\frac{105-x}{95}+4=0\)

\(\Leftrightarrow\)\(\left(\frac{108-x}{92}+1\right)+\left(\frac{107-x}{93}+1\right)+\left(\frac{106-x}{94}+1\right)+\left(\frac{105-x}{95}+1\right)+\left(4-4\right)=0\)

\(\Leftrightarrow\)\(\frac{200-x}{92}+\frac{200-x}{93}+\frac{200-x}{94}+\frac{200-x}{95}=0\)

\(\Leftrightarrow\)\(\left(200-x\right)\left(\frac{1}{92}+\frac{1}{93}+\frac{1}{94}+\frac{1}{95}\right)=0\)

Vì \(\frac{1}{92}+\frac{1}{93}+\frac{1}{94}+\frac{1}{95}\ne0\)

\(\Rightarrow\)\(200-x=0\)

\(\Rightarrow\)\(x=200\)

Vậy \(x=200\)

Chúc bạn học tốt ~

x=-100

\(\frac{x+5}{95}+\frac{x+6}{94}+\frac{x+7}{93}+\frac{x+8}{92}+\frac{x+9}{91}=-5\)

\(\left(\frac{x+5}{95}+1\right)+\left(\frac{x+6}{94}+1\right)+\left(\frac{x+7}{93}+1\right)+\left(\frac{x+8}{92}+1\right)+\left(\frac{x+9}{91}+1\right)=-5+5=0\)

x=100

k hộ với

\(\frac{x+1}{96}+\frac{x+2}{95}=\frac{x+3}{94}+\frac{x+4}{93}\)

\(\Rightarrow\left(\frac{x+1}{96}+1\right)+\left(\frac{x+2}{95}+1\right)=\left(\frac{x+3}{94}+1\right)+\left(\frac{x+4}{93}+1\right)\)

\(\Rightarrow\frac{x+97}{96}+\frac{x+97}{95}=\frac{x+97}{94}+\frac{x+97}{93}\)

\(\Rightarrow\frac{x+97}{96}+\frac{x+97}{95}-\frac{x+97}{94}-\frac{x+97}{93}=0\)

\(\Rightarrow\left(x+97\right)\left(\frac{1}{96}+\frac{1}{95}-\frac{1}{94}-\frac{1}{93}\right)=0\)

Mà \(\frac{1}{96}+\frac{1}{95}-\frac{1}{94}-\frac{1}{93}\ne0\)

\(\Rightarrow x+97=0\)

\(\Rightarrow x=-97\)

Vậy x = -97

Có : \(\frac{x+1}{96}+\frac{x+2}{95}=\frac{x+3}{94}+\frac{x+4}{93}\)

\(\Leftrightarrow\)\(\left(\frac{x+1}{96}+1\right)+\left(\frac{x+2}{95}+1\right)\)= \(\left(\frac{x+3}{94}+1\right)+\left(\frac{x+4}{93}+1\right)\)

\(\Leftrightarrow\) \(\frac{x+97}{96}+\frac{x+97}{95}=\frac{x+97}{94}+\frac{x+97}{93}\)

\(\Leftrightarrow\) \(\frac{x+97}{96}+\frac{x+97}{95}-\frac{x+97}{94}-\frac{x+97}{93}=0\)

\(\Leftrightarrow\) \(\left(x+97\right)\left(\frac{1}{96}+\frac{1}{95}-\frac{1}{94}-\frac{1}{93}\right)=0\)

\(\Leftrightarrow\) \(\left(x+97\right)=0\) ( \(\frac{1}{96}+\frac{1}{95}-\frac{1}{94}-\frac{1}{93}\)) \(\ne0\)

\(\Leftrightarrow\)\(x=-97\)

Vậy \(x=-97\)

\(\frac{x+1}{94}+\frac{x+2}{93}+\frac{x+3}{92}=\frac{x+4}{91}+\frac{x+5}{90}+\frac{x+6}{89}\)

\(\Leftrightarrow\frac{x+1}{94}+1+\frac{x+2}{93}+1+\frac{x+3}{92}+1=\frac{x+4}{91}+1+\frac{x+5}{90}+1+\frac{x+6}{89}+1\)

\(\Leftrightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}=\frac{x+95}{91}+\frac{x+95}{90}+\frac{x+95}{89}\)

\(\Leftrightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}-\frac{x+95}{91}-\frac{x+95}{90}-\frac{x+95}{89}=0\)

\(\Leftrightarrow\left(x+95\right)\left(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\right)=0\)

\(\Leftrightarrow x+95=0\).Do \(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\ne0\)

\(\Leftrightarrow x=-95\)

(x+1)/94 + ( x+2)/93 + ( x+3)/92.......

= ................ + ( x+6)/89 
<=> (x+1)/94 + 1 + ( x+2)/93 +1 .........

=.............. cộng 1 nhá 
<=> (x+95)/94 + ( x+96) / 93 + ( x+95)/92

= ( x+95)/91 + ( x+95)/90 + ( x+95)/89 
<=> ( x+95) ( 1/94 +1/93 +1/92 )

= ( x+95) ( 1/91 +1/90 +1/89) 
<=> ( x+95) ( 1/94 +1/93 +1/92 - 1/91 - 1/90 - 1/89 ) 
<=> x+95 =0 
<=>x = -95 
Vậy :x = -95

a) \(\frac{x+1}{94}+\frac{x+2}{93}+\frac{x+3}{92}=\frac{x+4}{91}+\frac{x+5}{90}+\frac{x+6}{89}\)

\(\Leftrightarrow\left(\frac{x+1}{94}+1\right)+\left(\frac{x+2}{93}+1\right)+\left(\frac{x+3}{92}+1\right)=\left(\frac{x+4}{91}+1\right)+\left(\frac{x+5}{90}+1\right)+\left(\frac{x+6}{89}+1\right)\)

\(\Leftrightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}-\frac{x+95}{91}-\frac{x+95}{90}-\frac{x+95}{89}=0\)

\(\Leftrightarrow\) \(\left(x+95\right)\left(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\right)=0\)

Vì \(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\ne0\)

\(\Rightarrow x+95=0\)

\(\Leftrightarrow x=-95\)

Vậy phương trình có một nghiệm x = -95

b) \(\frac{x-1}{59}+\frac{x-2}{58}+\frac{x-3}{57}=\frac{x-4}{56}+\frac{x-5}{55}+\frac{x-6}{54}\)

\(\Leftrightarrow\left(\frac{x-1}{59}-1\right)+\left(\frac{x-2}{58}-1\right)+\left(\frac{x-3}{57}-1\right)=\left(\frac{x-4}{56}-1\right)+\left(\frac{x-5}{55}-1\right)+\left(\frac{x-6}{54}-1\right)\)

\(\Leftrightarrow\frac{x-60}{59}+\frac{x-60}{58}+\frac{x-60}{57}-\frac{x-60}{56}-\frac{x-60}{55}-\frac{x-60}{54}=0\)

\(\Leftrightarrow\left(x-60\right)\left(\frac{1}{59}+\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}-\frac{1}{54}\right)=0\)

Vì \(\frac{1}{59}+\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}-\frac{1}{54}\ne0\)

\(\Rightarrow x-60=0\)

\(\Leftrightarrow x=60\)

Vậy phương trình có một nghiệm x = 60

a) \(\frac{x+1}{94}+\frac{x+2}{93}+\frac{x+3}{92}=\frac{x+4}{91}+\frac{x+5}{90}+\frac{x+6}{89}\)

\(\Rightarrow\left(\frac{x+1}{94}+1\right)+\left(\frac{x+2}{93}+1\right)+\left(\frac{x+3}{92}+1\right)=\left(\frac{x+4}{91}+1\right)+\left(\frac{x+5}{90}+1\right)+\left(\frac{x+6}{89}+1\right)\)

\(\Rightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}=\frac{x+95}{91}+\frac{x+95}{90}+\frac{x+95}{89}\)

\(\Rightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}-\frac{x+95}{91}-\frac{x+95}{90}-\frac{x+95}{89}=0\)

\(\Rightarrow\left(x+95\right)\left(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\right)=0\)

Mà \(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\ne0\)

\(\Rightarrow x+95=0\)

\(\Rightarrow x=-95\)

Vậy x = -95

b) \(\frac{x-1}{59}+\frac{x-2}{58}+\frac{x-3}{57}=\frac{x-4}{56}+\frac{x-5}{55}+\frac{x-6}{54}\)

\(\Rightarrow\left(\frac{x-1}{59}-1\right)+\left(\frac{x-2}{58}-1\right)+\left(\frac{x-3}{57}-1\right)=\left(\frac{x-4}{56}-1\right)+\left(\frac{x-5}{55}-1\right)+\left(\frac{x-6}{54}-1\right)\)

\(\Rightarrow\frac{x-60}{59}+\frac{x-60}{58}+\frac{x-60}{57}-\frac{x-60}{56}-\frac{x-5}{55}-\frac{x-6}{54}=0\)

\(\Rightarrow\left(x-60\right)\left(\frac{1}{59}+\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}-\frac{1}{54}\right)=0\)

Mà \(\frac{1}{59}+\frac{1}{58}+\frac{1}{57}-\frac{1}{56}-\frac{1}{55}-\frac{1}{54}\ne0\)

\(\Rightarrow x-60=0\)

\(\Rightarrow x=60\)

Vậy x = 60

\(\Leftrightarrow\frac{x+8}{92}+1+\frac{x+7}{93}+1+\frac{x+6}{94}+1\ge\frac{x+2}{98}+1+\frac{x+3}{97}+1+\frac{x+4}{96}+1\)

\(\Leftrightarrow\frac{x+100}{92}+\frac{x+100}{93}+\frac{x+100}{94}\ge\frac{x+100}{98}+\frac{x+100}{97}+\frac{x+100}{96}\)

\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{92}-\frac{1}{98}+\frac{1}{93}-\frac{1}{97}+\frac{1}{94}-\frac{1}{96}\right)\ge0\)

\(\Leftrightarrow\left(x+100\right)\left(\frac{6}{92.98}+\frac{4}{93.97}+\frac{2}{94.96}\right)\ge0\)

\(\Leftrightarrow x+100\ge0\Rightarrow x\ge-100\)

a)\(\frac{x}{108}=\frac{-7}{9}.\frac{5}{6}\)

\(\frac{x}{108}=\frac{-35}{54}\)

\(\frac{x}{108}=\frac{-70}{108}\)

\(x=-70\)

b) 

\(\left(x-3\right)^3-2\left(x-1\right)=x\left(x-2\right)^2-5x^2\)

\(\Leftrightarrow x^3-9x^2+27x-27-2x+2=x^3-4x^2+4x-5x^2\)

\(\Leftrightarrow27x-2x-4x-27+2=0\)

\(\Leftrightarrow21x=25\)

\(\Leftrightarrow x=\frac{25}{21}\)

Hết ý tưởng,phá tung ra,sai chỗ nào tự sửa nhé !

\(\frac{\left(x+1\right)^2}{3}+\frac{\left(x+2\right)\left(x-3\right)}{2}=\frac{\left(5x-1\right)\left(x-4\right)}{6}+\frac{28}{3}\)

\(\Leftrightarrow\frac{2\left(x+1\right)^2+3\left(x+2\right)\left(x-3\right)-\left(5x-1\right)\left(x-4\right)}{6}=\frac{28}{3}\)

\(\Leftrightarrow\frac{2x^2+4x+2+3x^2-3x-18-5x^2-21x+4}{6}=\frac{28}{3}\)

\(\Leftrightarrow\frac{\left(4x-3x-21x\right)+\left(2-18+4\right)}{6}=\frac{56}{6}\)

\(\Leftrightarrow-20x-12=56\)

\(\Leftrightarrow-20x=68\)

\(\Leftrightarrow x=-\frac{17}{5}\)

Tự check lại nhá

\(\frac{x+1}{94}+\frac{x+2}{93}+\frac{x+3}{92}=\frac{x+4}{91}+\frac{x+5}{90}+\frac{x+6}{89}\)

\(\Leftrightarrow\left(\frac{x+1}{94}+1\right)+\left(\frac{x+2}{93}+1\right)+\left(\frac{x+3}{92}+1\right)=\left(\frac{x+4}{91}+1\right)+\left(\frac{x+5}{90}+1\right)+\left(\frac{x+6}{89}+1\right)\)

\(\Leftrightarrow\frac{x+95}{94}+\frac{x+95}{93}+\frac{x+95}{92}=\frac{x+95}{91}+\frac{x+95}{90}+\frac{x+95}{89}\)

\(\Leftrightarrow\left(x+95\right)\left(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}\right)=0\)

Ta dễ thấy \(\frac{1}{94}+\frac{1}{93}+\frac{1}{92}-\frac{1}{91}-\frac{1}{90}-\frac{1}{89}< 0\) nên

\(x+95=0\Leftrightarrow x=-95\)