Find the value of x such that \(\frac{x-7}{6}+\frac{x-11}{10}=\frac{x-8}{7}+\frac{x-10}{9}\)
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Answer: .x=..
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![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x-7}{6}+\frac{x-11}{10}=\frac{x-8}{7}+\frac{x-10}{9}\)
\(\Rightarrow\left(\frac{x-7}{6}+1\right)+\left(\frac{x-11}{10}+1\right)=\left(\frac{x-8}{7}+1\right)+\left(\frac{x-10}{9}+1\right)\)
\(\Rightarrow\frac{x-1}{6}+\frac{x-1}{10}-\frac{x-1}{7}-\frac{x-1}{9}=0\)
\(\left(x-1\right).\left(\frac{1}{6}+\frac{1}{10}-\frac{1}{7}-\frac{1}{9}\right)=0\)
\(\Rightarrow x-1=0\Rightarrow x=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x\ne-\frac{7}{2};x\ne-3\)
\(\Rightarrow3\left(3x+9\right)=5\left(2x+7\right)\)
\(\Rightarrow9x+27=10x+35\)
\(\Rightarrow10x-9x=27-35\)
\(\Rightarrow x=-8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{a+1}-\frac{1}{a+7}=\frac{a+7}{\left(a+1\right)\left(a+7\right)}-\frac{a+1}{\left(a+1\right)\left(a+7\right)}=\frac{6}{\left(a+1\right)\left(a+7\right)}\)
=>x+7=6
=>x=6-7
=>x=-1
vậy x=-1
\(\frac{1}{a+1}-\frac{1}{a+7}=\frac{\left(a+7\right)-\left(a+1\right)}{\left(a+1\right)\left(a+7\right)}=\frac{6}{\left(a+1\right)\left(a+7\right)}\)=> x + 7 = 6 => x = -1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x}{10}=\frac{y}{6}=\frac{z}{21}\)và \(5x+y-2z=28\)
Ta có
\(\frac{x-7}{6}+1+\frac{x-11}{10}+1=\frac{x-8}{7}+1+\frac{x-10}{9}+1\)
\(\frac{x-1}{6}+\frac{x-1}{10}-\frac{x-1}{7}-\frac{x-1}{9}=0\)
<=>\(\left(x-1\right)\left(\frac{1}{6}+\frac{1}{10}-\frac{1}{7}-\frac{1}{11}\right)=0\)
=>x-1=0
<=>x=1