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a, \(\frac{x+9}{10}+\frac{x+10}{9}=\frac{9}{x+10}+\frac{10}{x+9}\)(1)
ĐKXĐ: \(\hept{\begin{cases}x+9\ne0\\x+10\ne0\end{cases}\Leftrightarrow\hept{\begin{cases}x\ne-9\\x\ne-10\end{cases}}}\)
(1)\(\Leftrightarrow\frac{9.\left(x+9\right)}{90}+\frac{10.\left(x+10\right)}{90}=\frac{9.\left(x+9\right)}{\left(x+9\right)\left(x+10\right)}+\frac{10.\left(x+10\right)}{\left(x+9\right)\left(x+10\right)}\)
\(\Leftrightarrow9.\left(x+9\right)+10.\left(x+10\right)=9.\left(x+9\right)+10.\left(x+10\right)\)
\(\Leftrightarrow9x+81+10x+100=9x+81+10x+100\)
\(\Leftrightarrow9x+10x-9x-10x=81+100-81-100\)
\(\Leftrightarrow0x=0\)
\(\Rightarrow x\in R\)trừ -9 và -10
ĐKXĐ: x≠-10; x≠-9
Ta có: \(\frac{x+9}{10}+\frac{x+10}{9}=\frac{10}{x+9}+\frac{9}{x+10}\)
Vậy: x=0
\(\frac{8}{x-8}+\frac{11}{x-11}=\frac{9}{x-9}+\frac{10}{x-10}\)<=> \(\frac{8}{x-8}+1+\frac{11}{x-11}+1=\frac{9}{x-9}+1+\frac{10}{x-10}+1\)
<=>\(\frac{8+x-8}{x-8}+\frac{11+x-11}{x-11}=\frac{9+x-9}{x-9}+\frac{10+x-10}{x-10}\)
<=>\(\frac{x}{x-8}+\frac{x}{x-11}=\frac{x}{x-9}+\frac{x}{x-10}\)
<=>\(\frac{x}{x-8}+\frac{x}{x-11}-\frac{x}{x-9}-\frac{x}{x-10}=0\)
<=>\(x\left(\frac{1}{x-8}+\frac{1}{x-11}-\frac{1}{x-9}-\frac{1}{x-10}\right)=0\)
=>\(\orbr{\begin{cases}x=0\\\frac{1}{x-8}+\frac{1}{x-11}-\frac{x}{x-9}-\frac{x}{x-10}=0\end{cases}}\)
đến đoạn bạn giải tiếp nhé
\(\frac{8}{x-8}+\frac{11}{x-11}=\frac{9}{x-9}+\frac{10}{x-10}\)
\(-537x^2+5054x=-541x^2+5092x\)
\(-537x^2+5054x+541x^2-5092x=0\)
\(4x^2-38x=0\)
\(x\left(2x-19\right)=0\)
\(\orbr{\begin{cases}x=0\\2x=19\end{cases}}\)
\(\orbr{\begin{cases}x=0\\x=\frac{19}{2}\end{cases}}\)
\(\Leftrightarrow\frac{9\left(X+9\right)\left(X+9\right)\left(X+10\right)+10\left(X+10\right)\left(X+10\right)\left(X+9\right)}{90\left(X+10\right)\left(X+9\right)}=\frac{9.90\left(X+9\right)+10.90\left(X+10\right)}{90\left(X+10\right)\left(X+9\right)}\)
\(\Rightarrow9\left(X+9\right)^2\left(X+10\right)+10\left(X+10\right)^2\left(X+9\right)=810\left(X+9\right)+900\left(X+10\right)\)
\(\Leftrightarrow\left(9X+90\right)\left(X^2+18X+81\right)+\left(10X+90\right)\left(X^2+20X+100\right)=810X+7290+900X+9000\)
\(\Leftrightarrow\)9X3+162X2+729X+90X2+1620X+7290+10X3+200X2+1000X+90X2+1800X+9000=1710X+16290
\(\Leftrightarrow\)19X3+542X2+5149X+16290=1710X+16290
\(\Leftrightarrow\)19X3+542X2=16290-16290+1710X-5149X
\(\Leftrightarrow\)19X3+542X2=-3439X
\(\Leftrightarrow\)19X3+542X2+3439X=0
RỒI GIẢI TIẾP
nốt đi bạn
Mk nghĩ nên giải theo cách này thì hay hơn ( mk mớp 7 thui nên bài làm mang tính chất tham khảo nhé )
Ta có :
\(\frac{x+9}{10}+\frac{x+10}{9}=\frac{9}{x+10}+\frac{10}{x+9}\)
\(\Leftrightarrow\)\(\left(\frac{x+9}{10}+1\right)+\left(\frac{x+10}{9}+1\right)=\left(\frac{9}{x+10}+1\right)+\left(\frac{10}{x+9}+1\right)\)
\(\Leftrightarrow\)\(\frac{x+19}{10}+\frac{x+19}{9}=\frac{x+19}{x+10}+\frac{x+19}{x+9}\)
\(\Leftrightarrow\)\(\frac{x+19}{10}+\frac{x+19}{9}-\frac{x+19}{x+10}-\frac{x+19}{x+9}=0\)
\(\Leftrightarrow\)\(\left(x+19\right)\left(\frac{1}{10}+\frac{1}{9}-\frac{1}{x+10}-\frac{1}{x+9}\right)=0\)
Xét trường hợp \(x=0\)
\(\Rightarrow\)\(\left(x+19\right)\left(\frac{1}{10}+\frac{1}{9}-\frac{1}{x+10}-\frac{1}{x+9}\right)=\left(x+19\right)\left(\frac{1}{10}+\frac{1}{9}-\frac{1}{10}-\frac{1}{9}\right)=\left(x+19\right).0=0\)
( NHẬN )
\(\Rightarrow\) Nếu \(x\ne0\) thì \(\frac{1}{10}+\frac{1}{9}-\frac{1}{x+10}-\frac{1}{x+9}\ne0\)
Xét trường hợp x nguyên dương ta có :
\(\frac{1}{10}>\frac{1}{x+10}\)
\(\frac{1}{9}>\frac{1}{x+9}\)
\(\Rightarrow\)\(\frac{1}{10}+\frac{1}{9}-\frac{1}{x+10}-\frac{1}{x+9}>0\)
Xét trường hợp x nguyên âm ta có :
\(\frac{1}{10}< \frac{1}{x+10}\)
\(\frac{1}{9}< \frac{1}{x+9}\)
\(\Rightarrow\)\(\frac{1}{10}+\frac{1}{9}-\frac{1}{x+9}-\frac{1}{x+10}< 0\)
Từ đó suy ra :
\(x+19=0\)
\(\Rightarrow\)\(x=-19\)
Vậy \(x=0\) hoặc \(x=-19\)
\(\frac{x+9}{10}+\frac{x+10}{9}=\frac{9}{x+10}+\frac{10}{x+9}\)
\(\Leftrightarrow\frac{x+9}{10}.90\left(x+9\right)\left(x+10\right)+\frac{x+10}{9}.90\left(x+9\right)\left(x+10\right)\)\(=\frac{9}{x+10}.90\left(x+9\right)\left(x+10\right)+\frac{10}{x+9}.90\left(x+9\right)\left(x+10\right)\)
\(\Leftrightarrow9\left(x+9\right)^2\left(x+10\right)+10\left(x+9\right)\left(x+10\right)^2=810\left(x+9\right)+900\left(x+10\right)\)
\(\Leftrightarrow19x^3+542x^2+5149x=1710x+16290\)
\(\Leftrightarrow19x^3+542x^2+5194x=1710x+16290-16290\)
\(\Leftrightarrow19x^3+542x^2+5149x=1710x\)
\(\Leftrightarrow19x^3+542x^2+5149x=1710x-1710x\)
\(\Leftrightarrow19x^3+542x^2+3439x=0\)
\(\Leftrightarrow19x^3+542x^2+3439x=x\left(19x^2+542+3439\right)\)
\(\Leftrightarrow x\left(x+19\right)\left(19x+181\right)=0\)
\(\Rightarrow\hept{\begin{cases}x=0\\x=-19\\x=-\frac{181}{19}\end{cases}}\)