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Qui đồng rồi khử mẫu, ta được:
\(4x+12.\left(27-x\right)=15x+5.\left(27-x\right)\)
\(\Leftrightarrow4x+324-12x=15x+135-5x\)
\(\Leftrightarrow4x-12x-15x+5x=135-324\)
\(\Leftrightarrow-18x=-189\Leftrightarrow x=\frac{21}{2}=10,5\)
Vậy x = 10,5
\(\frac{x}{15}+\frac{27-x}{5}=\frac{x}{4}+\frac{27-x}{12}\)
\(\frac{x}{15}+\frac{3\left(27-x\right)}{15}=\frac{3x}{12}+\frac{27-x}{12}\)
\(\frac{x}{15}+\frac{81-3x}{15}=\frac{3x}{12}+\frac{27-x}{12}\)
\(\frac{x+81-3x}{15}=\frac{3x+27-x}{12}\)
\(\frac{-2x+81}{15}=\frac{2x+27}{12}\)
\(12\left(-2x+81\right)=15\left(2x+27\right)\)
\(-24x+972=30x+405\)
\(972-405=30x+24x\)
\(567=54x\)
\(x=567:54\)
\(x=10,5\)
Đặt \(A=\frac{2^{19}\cdot27^3+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\)
\(A=\frac{2^{19}\cdot\left(3^3\right)^3+15\cdot\left(2^2\right)^9\cdot\left(3^2\right)^4}{6^9\cdot2^9\cdot2+12^{10}}\)
\(A=\frac{2^{19}\cdot3^9+15\cdot2^{18}\cdot3^8}{12^9\cdot2+12^9\cdot12}=\frac{\left(2^{18}\cdot3^8\right)\cdot6+\left(2^{18}\cdot3^8\right)\cdot15}{12^9\cdot\left(2+12\right)}\)
\(A=\frac{\left(2^{18}\cdot3^8\right)\cdot\left(6+15\right)}{12^9\cdot14}=\frac{2^{18}\cdot3^8\cdot21}{12^9\cdot14}=\frac{2^{18}\cdot3^8\cdot7\cdot3}{2^{18}\cdot3^9\cdot7\cdot2}=\frac{3^8\cdot3}{3^8\cdot3\cdot2}\)
\(A=\frac{1}{2}\)
Đặt \(B=\frac{4}{35}+\frac{4}{63}+\frac{4}{99}+\frac{4}{143}+\frac{4}{195}=\frac{4}{5\cdot7}+\frac{4}{7\cdot9}+\frac{4}{9\cdot11}+\frac{4}{11\cdot13}+\frac{4}{13\cdot15}\)
\(B=\frac{1}{2}\left(\frac{4}{5}-\frac{4}{7}+\frac{4}{7}-\frac{4}{9}+...+\frac{4}{13}-\frac{4}{15}\right)\)
\(B=\frac{1}{2}\left(\frac{4}{5}-\frac{4}{15}\right)\)mà \(\frac{4}{5}-\frac{4}{15}< 1\Leftrightarrow\frac{1}{2}\left(\frac{4}{5}-\frac{4}{15}\right)< \frac{1}{2}\Leftrightarrow B< A\)
a) x - 2/3 = -5/12
=> x = -5/12 + 2/3
=> x = 1/4
b) \(\frac{x+5}{3}=\frac{5}{9}\)
=> \(\frac{3\left(x+5\right)}{9}=\frac{5}{9}\)
=> 3(x + 5) = 5
=> x + 5 = 5 : 3
=> x + 5 = 5/3
=> x = 5/3 - 5
=> x = 20/3
c) \(\frac{x-2}{27}=\frac{3}{x-2}\)
=> (x - 2)(x - 2) = 27 . 3
=> (x - 2)2 = 81
=> (x - 2)2 = 92
=> \(\orbr{\begin{cases}x-2=9\\x-2=-9\end{cases}}\)
=> \(\orbr{\begin{cases}x=11\\x=-7\end{cases}}\)
Vậy ...
Ta có:
\(\frac{y}{27}=\frac{-42}{54}\)
\(\Rightarrow y=\frac{-42.27}{54}=-21\)
Lại có:
\(\frac{7}{x}=\frac{-21}{27}\)
\(\Rightarrow x=\frac{7.27}{-21}=-9\)
Vậy .....
Tìm x:
\(\frac{7}{x}\)= \(\frac{-42}{54}\)
\(\Rightarrow\)\(\frac{7.\left(-6\right)}{x.\left(-6\right)}\) = \(\frac{-42}{54}\)
\(\Rightarrow\)\(x.\left(-6\right)=54\)
\(\Rightarrow x=54\div\left(-6\right)\)
\(\Rightarrow x=-9\)
Tìm y:
\(\frac{y}{27}=\frac{-42}{54}\)
\(\Rightarrow\frac{y.2}{27.2}=\frac{-42}{54}\)
\(\Rightarrow y.2=-42\)
\(\Rightarrow y=\left(-42\right)\div2\)
\(\Rightarrow y=-21\)
\(Họctốtnhé\)
\(x-\frac{27}{12}.\frac{5}{11}=\frac{1}{2}-\frac{5}{11}.\frac{5}{4}\)
\(x-\frac{45}{44}=\frac{1}{2}-\frac{25}{44}\)
\(x-\frac{45}{44}=\frac{22}{44}-\frac{25}{44}\)
\(x-\frac{45}{44}=\frac{-3}{44}\)
\(x=\frac{-3}{44}+\frac{45}{44}\)
\(x=\frac{42}{44}\)
\(x=\frac{21}{22}\)