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a, Ta có : \(\frac{xy^2}{yz}=\frac{xyy}{yz}=\frac{xy}{z}.\frac{y}{y}=\frac{xy}{z}.1=\frac{xy}{z}\)
b, Ta có : \(\frac{7x-21}{14x-42}=\frac{7\left(x-3\right)}{14\left(x-3\right)}=\frac{7}{14}=\frac{1}{2}\)
c, Ta có : \(\frac{\overline{ab}}{abab}=\frac{10a+b}{1000a+100b+10a+b}=\frac{10a+b}{100\left(10a+b\right)+1\left(10a+b\right)}\)
\(=\frac{10a+b}{\left(100+1\right)\left(10a+b\right)}=\frac{1}{101}\)
d, Ta có : \(\frac{\frac{4}{11}-\frac{12}{31}+\frac{16}{59}}{\frac{3}{11}-\frac{9}{31}+\frac{12}{59}}=\frac{4\left(\frac{1}{11}-\frac{3}{31}+\frac{4}{59}\right)}{3\left(\frac{1}{11}-\frac{3}{31}+\frac{4}{59}\right)}=\frac{4}{3}\)
Bài làm:
Ta có: \(\frac{ab0ab}{cd0cd}=\frac{ab.1001}{cd.1001}=\frac{ab}{cd}\)
(Với ab ; cd là các số)
=> đpcm
\(\frac{\frac{4}{11}-\frac{12}{31}+\frac{16}{59}}{\frac{3}{11}-\frac{9}{31}+\frac{12}{59}}=\frac{4.\left(\frac{1}{11}-\frac{3}{31}+\frac{4}{59}\right)}{3.\left(\frac{1}{11}-\frac{3}{31}+\frac{4}{59}\right)}=\frac{4}{3}\)( vì \(\frac{1}{11}-\frac{3}{31}+\frac{4}{59}\ne0\))
Bài làm:
Ta có: \(\frac{\frac{4}{11}-\frac{12}{31}+\frac{16}{59}}{\frac{3}{11}-\frac{9}{31}+\frac{12}{95}}=\frac{4\left(\frac{1}{11}-\frac{3}{31}+\frac{4}{59}\right)}{3\left(\frac{1}{11}-\frac{3}{31}+\frac{4}{59}\right)}=\frac{4}{3}\)
a)Ta có \(\hept{\begin{cases}\frac{-22}{55}=\frac{-22:11}{55:11}=\frac{-2}{3}\\\frac{-26}{65}=\frac{-26:13}{65:13}=\frac{-2}{3}\end{cases}}\)=> \(\frac{-22}{55}=\frac{-26}{65}\)
b) Ta có : \(\hept{\begin{cases}\frac{114}{122}=\frac{114:2}{112:2}=\frac{57}{61}\\\frac{5757}{6161}=\frac{5757:101}{6161:101}=\frac{57}{61}\end{cases}\Rightarrow\frac{114}{122}=\frac{5757}{6161}}\)
d) \(\frac{x}{-9}=\left(\frac{2}{6}\right)^2\)
\(\Rightarrow\frac{x}{-9}=\frac{2}{6}.\frac{2}{6}\)
\(\Rightarrow\frac{x}{-9}=\frac{4}{36}\)
\(\Rightarrow\frac{x}{-9}=\frac{1}{9}\)
\(\Rightarrow\frac{-x}{9}=\frac{1}{9}\)
\(\Rightarrow-x=1\)
\(\Rightarrow x=1\)
e) \(\frac{a}{b}+\frac{3}{6}=0\)
\(\Rightarrow\frac{a}{b}=0-\frac{3}{6}\)
\(\Rightarrow\frac{a}{b}=0-\frac{1}{2}\)
\(\Rightarrow\frac{a}{b}=\frac{-1}{2}\)
\(\Rightarrow a=-1;b=2\)
ĐK : x \(\ne\)3
\(\frac{7x-21}{14x-42}=\frac{1}{2}\Leftrightarrow14x-42=14x-42\)
\(\Leftrightarrow0=0\)*đúng* | Vậy vô nghiệm, mk chưa hc nên cx ko biết KL
\(\frac{7x-21}{14x-42}=\frac{7x-21}{2\left(7x-21\right)}=\frac{1}{2}=VP\)( ddpcm )