\(\frac37.\frac{3}{26}-\frac{1}{14}.\frac{-4}{13}\)
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Có: \(\frac{y-2}{3}=\frac{2y-4}{6}\)
\(\frac{z-3}{4}=\frac{3z-9}{12}\)
Suy ra\(\frac{x-1}{2}=\frac{2y-4}{6}=\frac{3z-9}{12}=\frac{\left(x-1\right)-\left(2y-4\right)+\left(3z-9\right)}{2-6+12}\)
\(=\frac{\left(x-2y+3z\right)-6}{8}=\frac{14-6}{8}=1\)
Vậy có \(\frac{x-1}{2};\frac{y-2}{3};\frac{z-3}{4}=1\)Thay vào có x=3; y=5; z=7

ta có \(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}=\frac{3\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}{5\left(\frac{1}{7}-\frac{1}{11}+\frac{1}{13}\right)}=\frac{3}{5}\)
và \(\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}+\frac{5}{8}-\frac{5}{6}}=\frac{2\left(\frac{1}{2.2}-\frac{1}{3.2}+\frac{1}{4.2}\right)}{5\left(\frac{1}{4}+\frac{1}{8}-\frac{1}{6}\right)}=\frac{2\left(\frac{1}{4}+\frac{1}{8}-\frac{1}{6}\right)}{5\left(\frac{1}{4}+\frac{1}{8}-\frac{1}{6}\right)}=\frac{2}{5}\)
Vậy \(\frac{\frac{3}{7}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}+\frac{5}{8}-\frac{5}{6}}=\frac{3}{5}+\frac{2}{5}=\frac{5}{5}=1\)
ĐS: 1

\(B=4\cdot\left(-\frac{1}{2}\right)^3:\left(\frac{4}{5}\right)^0\cdot\frac{1}{2}-\frac{\frac{3}{5}-\frac{3}{9}+\frac{3}{13}}{\frac{7}{5}-\frac{7}{9}+\frac{7}{13}}\)
\(=4\cdot\frac{-1}{8}:1\cdot\frac{1}{2}-\frac{3\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{13}\right)}{7\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{13}\right)}\)
\(=-\frac{1}{4}-\frac{3}{7}=-\frac{19}{28}\)

\(\frac{x+1}{2x+1}=\frac{0,5x+2}{x+3}\)
\(\left(x+1\right)\left(x+3\right)=\left(0,5x+2\right)\left(2x+1\right)\)
\(x^2+4x+3=x^2+4,5x+2\)
\(x^2-x^2+4x-4,5x-2+3=0\)
\(1-0,5x=0\)
\(x=2\)

a,\(\frac{25}{42}-\frac{20}{63}=\frac{5}{18}\)
b,\(\frac{9}{50}-\frac{13}{75}-\frac{1}{6}\)
=\(\frac{1}{150}-\frac{1}{6}\)
=\(-\frac{4}{25}\)
c,\(\frac{2}{15}+\frac{-2}{65}-\frac{4}{39}\)
=\(\frac{32}{195}-\frac{4}{39}\)
=\(\frac{4}{65}\)
a,=75/126-40/126=35/126=5/18
b,=27/150-26/150-25/150=-4/25
c,=26/195+-6/195-20/195=0

Giải:
Vì
Nên ta phải chứng minh:
=> ( điều phải chứng minh)
\(\frac{1}{14}\)
\(\frac{3}{7} . \frac{3}{26} - \frac{1}{14} . \frac{- 4}{13}\)
\(=\frac{9}{182}-\left(-\frac{4}{182}\right)\)
\(=\frac{9}{182}+\frac{4}{182}\)
\(=\frac{13}{182}=\frac{1}{14}\)