\(y=\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}\)
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Ta có:\(\frac{3^{10}\cdot\left(-5\right)\cdot21}{\left(-5\right)^{20}\cdot3^{12}}\)
\(=\frac{3^{10}\cdot\left(-5\right)\cdot21}{\left(-5\right)^{19}\cdot\left(-5\right)\cdot3^{12}}\)
\(=\frac{3\cdot7}{\left(-5\right)^{19}\cdot3^2}\)
\(=\frac{7}{\left(-5\right)^{19}\cdot3}\)
\(=\frac{3^{10}.\left(-5\right)^{20}.\left(-5\right)^1}{\left(-5\right)^{20}.3^{10}.3^2}\)\(=\frac{\left(-5\right)^1}{3^2}\)\(=\frac{-5}{9}\)
Hok tốt !
\(\frac{3^{10}.\left(-5\right)^{20}.\left(-5\right)^1}{\left(-5\right)^{20}.3^{10}.3^2}=\frac{-5}{3^2}=\frac{-5}{9}\)
\(\frac{3^{10}.\left(-5\right)^{20}.\left(-5\right)}{3^{10}.3^2.\left(-5\right)^{20}}=\frac{-5}{3^2}=\frac{-5}{9}\)
T I C K cho mình nha cảm ơn chúc bạn học tốt nha
\(\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\frac{3^{10}.\left(-5\right)^{20}.\left(-5\right)}{\left(-5\right)^{20}.3^{10}.3^2}=\frac{-5}{3^2}=-\frac{5}{9}\)
\(\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\frac{3^{10}.\left(-5\right)^{20}.\left(-5\right)}{\left(-5\right)^{20}.3^{10}.3^2}=\frac{-5}{3^2}=\frac{-5}{9}\)
$\textbf{b)}$
$\text{Điều kiện: }x\ne1,\ 3,\ 8,\ 20.$
$\dfrac2{(x-1)(x-3)}+\dfrac5{(x-3)(x-8)}+\dfrac{12}{(x-8)(x-20)}-\dfrac1{x-20}=-\dfrac34$
$\Leftrightarrow\left(\dfrac1{x-3}-\dfrac1{x-1}\right)+\left(\dfrac1{x-8}-\dfrac1{x-3}\right)+\left(\dfrac1{x-20}-\dfrac1{x-8}\right)-\dfrac1{x-20}=-\dfrac34$
$\Leftrightarrow-\dfrac1{x-1}=-\dfrac34$
$\Leftrightarrow\dfrac1{x-1}=\dfrac34$
$\Leftrightarrow4=3(x-1)$
$\Leftrightarrow3x=7$
$\Leftrightarrow x=\dfrac73.$
$\textbf{a)}$
Điều kiện: $x\ne-2,\,-5,\,-10,\,-17.$
$\dfrac3{(x+2)(x+5)}+\dfrac5{(x+5)(x+10)}+\dfrac7{(x+10)(x+17)}=\dfrac{x}{(x+2)(x+17)}$
$\Leftrightarrow\left(\dfrac1{x+2}-\dfrac1{x+5}\right)+\left(\dfrac1{x+5}-\dfrac1{x+10}\right)+\left(\dfrac1{x+10}-\dfrac1{x+17}\right)=\dfrac{x}{(x+2)(x+17)}$
$\Leftrightarrow\dfrac1{x+2}-\dfrac1{x+17}=\dfrac{x}{(x+2)(x+17)}$
$\Leftrightarrow\dfrac{x+17-x-2}{(x+2)(x+17)}=\dfrac{x}{(x+2)(x+17)}$
$\Leftrightarrow\dfrac{15}{(x+2)(x+17)}=\dfrac{x}{(x+2)(x+17)}$
$\Leftrightarrow x=15.$
\(y=\frac{3^{10}.\left(-5\right)^2}{\left(-5\right)^{20}.3^{12}}=\frac{1.1}{5^{18}.3^{10}}=\frac{1}{5^8.5^{10}.3^{10}}=\frac{1}{5^5.15^{10}}\)