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a) \(\frac{11}{10,5}=\frac{6,32}{-x}\)
\(6,32:\frac{11}{10,5}=x\)
\(\frac{1659}{275}=x\)
b) \(\frac{x-1}{x+5}=\frac{6}{7}\)
\(\Rightarrow7x-7=6x+30\)
\(7x-6x=30+7\)
\(x=37\)
c) \(\frac{x^2}{6}=\frac{24}{25}\)
\(x^2=\frac{144}{25}\)
\(x=\frac{12}{5}\)
d) \(x:0,16=9:x\)
\(\frac{x}{0,16}=\frac{9}{x}\)
\(x^2=1,44\)
\(x=1,2\)
\(\frac{x-6}{7}+\frac{x-7}{8}+\frac{x-8}{9}=\frac{x-9}{10}+\frac{x-10}{11}+\frac{x-11}{12}\)
\(\Leftrightarrow\left(\frac{x-6}{7}+1\right)+\left(\frac{x-7}{8}+1\right)+\left(\frac{x-8}{9}+1\right)=\left(\frac{x-9}{10}+1\right)+\left(\frac{x-10}{11}+1\right)+\left(\frac{x-11}{12}+1\right)\)
\(\Leftrightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}=\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}\)
\(\Leftrightarrow\frac{x+1}{7}+\frac{x+1}{8}+\frac{x+1}{9}-\frac{x+1}{10}-\frac{x+1}{11}-\frac{x+1}{12}=0\)
\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\right)=0\)
\(\Leftrightarrow x+1=0\)( \(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\ne0\))
\(\Leftrightarrow x=-1\)
Vậy x=-1
mỗi phân số + 1 thì sẽ có tử chung là x + 1
chuyển vế có \(\left(x+1\right)\left(\frac{1}{7}+\frac{1}{8}+\frac{1}{9}-\frac{1}{10}-\frac{1}{11}-\frac{1}{12}\right)\)) =0
mà tổng các phân số kia khác 0 nên x+1 bằng 0
=> x=-1
\(\frac{11}{13}-\left(\frac{5}{42}-x\right)=-\left(\frac{15}{28}-\frac{11}{13}\right)\)
\(\left(\frac{5}{42}-x\right)=\frac{11}{13}-\left(-\frac{15}{28}-\frac{11}{13}\right)\)
\(\frac{5}{42}-x\)= \(\frac{11}{13}-\left(-\frac{503}{364}\right)\)
\(\frac{5}{42}-x\)= \(\frac{811}{364}\)
\(x=\frac{5}{42}-\frac{811}{364}\)
\(x=-\frac{329}{156}\)
Phần tìm x tự tính ra
\(\frac{x+2}{11}+\frac{x+2}{12}+\frac{x+2}{13}-\frac{x+2}{14}-\frac{x+2}{15}=0\\ \Leftrightarrow\left(x+2\right)\left(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}-\frac{1}{14}-\frac{1}{15}\right)=0\\ \Rightarrow x+2=0\Leftrightarrow x=-2\)
\(\frac{x+32}{11}+\frac{x+23}{12}=\frac{x+38}{13}+\frac{x+27}{14}\)
\(\Rightarrow\)\(\frac{x+32}{11}-3+\frac{x+23}{12}-2=\frac{x+38}{13}-3+\frac{x+27}{14}-2\)
\(\Rightarrow\frac{x-1}{11}+\frac{x-1}{12}=\frac{x-1}{13}+\frac{x-1}{14}\)
\(\Rightarrow\frac{x-1}{11}+\frac{x-1}{12}-\frac{x-1}{13}-\frac{x-1}{14}=0\)
\(\Rightarrow\left(x-1\right)\left(\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)
\(\Rightarrow x-1=0\)(Vì \(\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0\))
\(\Rightarrow x=1\)
Vậy:x=1
\(\frac{x+2}{10^{10}}+\frac{x+2}{11^{11}}=\frac{x +2}{12^{12}}+\frac{x+2}{13^{13}}\)
\(\Leftrightarrow\frac{x+2}{10^{10}}+\frac{x+2}{11^{11}}-\left(\frac{x+2}{12^{12}}+\frac{x+2}{13^{13}}\right)=0\)
\(\Leftrightarrow\frac{x+2}{10^{10}}+\frac{x+2}{11^{11}}-\frac{x+2}{12^{12}}-\frac{x+2}{13^{13}}=0\)
\(\Leftrightarrow\left(x+2\right).\left(\frac{1}{10^{10}}+\frac{1}{11^{11}}+\frac{1}{12^{12}}+\frac{1}{13^{13}}\right)=0\)
Vì \(\left(\frac{1}{10^{10}}+\frac{1}{11^{11}}+\frac{1}{12^{12}}+\frac{1}{13^{13}}\right)\ne0\)nên \(x+2=0\Rightarrow x=-2\)
<=>\(\frac{x+2}{10^{10}}+\frac{x+2}{11^{11}}-\frac{x+2}{12^{12}}-\frac{x+2}{13^{13}}=0\)
<=>\(\left(x+2\right)\left(\frac{1}{10^{10}}+\frac{1}{11^{11}}-\frac{1}{12^{12}}-\frac{1}{13^{13}}\right)=0\)
Vì \(\frac{1}{10^{10}}+\frac{1}{11^{11}}-\frac{1}{12^{12}}-\frac{1}{13^{13}}>0\)
=> \(x+2=0\)
<=>\(x=-2\)
\(\frac{11}{10,5}=\frac{6,32}{x}\Rightarrow x=\frac{6,32.10,5}{11}=\frac{1659}{275}\)
\(\frac{11}{10,5}=\frac{6,32}{x}\)
\(\Rightarrow11.x=6,32.10,5\)
\(\Rightarrow11.x=66,36\)
\(\Rightarrow x=66,36:11\)
\(\Rightarrow x=\frac{1659}{275}\)
Vậy \(x=\frac{1659}{275}.\)
Chúc bạn học tốt!