4/ Rút gọn
P= 212 . 35 - 46 . 36
212 . 93 + 84 . 36
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\(=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\sqrt{x}}-3+\sqrt{x}\)
\(=\sqrt{x}+2-3+\sqrt{x}=2\sqrt{x}-1\)
(1) 24 : 4 + 36 : 4
= ( 24 + 36 ) : 4
= 60 : 4
= 15
(2) 84 : 7 – 35 : 7
= ( 84 – 35 ) : 7
= 49 : 7
= 7
Chúc bạn học tốt nhe >w<
a; \(\dfrac{9}{27}\) + \(\dfrac{7}{-49}\)
= \(\dfrac{1}{3}\) - \(\dfrac{1}{7}\)
= \(\dfrac{7}{21}\) - \(\dfrac{3}{21}\)
= \(\dfrac{4}{21}\)
b; - \(\dfrac{12}{10}\) + \(\dfrac{-25}{30}\)
= - \(\dfrac{6}{5}\) - \(\dfrac{5}{6}\)
= -\(\dfrac{36}{30}\) - \(\dfrac{25}{30}\)
= \(\dfrac{-61}{30}\)
c; \(\dfrac{-20}{35}\) + \(\dfrac{-16}{-24}\)
= - \(\dfrac{4}{7}\) + \(\dfrac{2}{3}\)
= - \(\dfrac{12}{21}\) + \(\dfrac{14}{21}\)
= \(\dfrac{2}{21}\)
d; - \(\dfrac{21}{77}\) + \(\dfrac{10}{-35}\)
= - \(\dfrac{3}{11}\) - \(\dfrac{2}{7}\)
= - \(\dfrac{21}{77}\) - \(\dfrac{22}{77}\)
= - \(\dfrac{43}{77}\)
\(=\dfrac{2^{12}\cdot3^4\left(3-1\right)}{2^{12}\cdot3^6}-\dfrac{5^{10}\cdot7^3\left(1-7\right)}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}\)
\(=\dfrac{-2}{9}-\dfrac{5\cdot\left(-6\right)}{9}=\dfrac{-2-5\cdot\left(-6\right)}{9}=\dfrac{-2+30}{9}=\dfrac{28}{9}\)
Với \(\left\{{}\begin{matrix}a\ge0\\a\ne1\end{matrix}\right.\)
\(P=\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right).\left(\dfrac{1-\sqrt{a}}{1-a}\right)^2\\ =\left(\dfrac{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}+a\right)}{1-\sqrt{a}}+\sqrt{a}\right).\left(\dfrac{1-\sqrt{a}}{\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)}\right)^2\\ =\left(1+\sqrt{a}+a+\sqrt{a}\right)\left(\dfrac{1}{1+\sqrt{a}}\right)^2\\ =\left[\left(1+\sqrt{a}\right)+\sqrt{a}\left(\sqrt{a}+1\right)\right]\left(\dfrac{1}{1+\sqrt{a}}\right)^2\\ =\dfrac{\left(1+\sqrt{a}\right)\left(1+\sqrt{a}\right).1^2}{\left(1+\sqrt{a}\right)^2}=1\)
P = \(2^{12}\cdot3^5-\left(2^2\right)^6\cdot3^5\cdot3\)
\(=2^{12}\cdot3^5-2^{12}\cdot3^5\cdot3\)
\(=2^{12}\cdot3^5\left(1-3\right)\)
\(=2^{12}\cdot-2\cdot3^5\)
\(=-2^{13}\cdot3^5\)
b)
\(=2^{12}\cdot\left(3^2\right)^3+\left(2^3\right)^4\cdot3^6\)
\(=2^{12}\cdot3^6+2^{12}\cdot3^6\)
\(=2\cdot2^{12}\cdot3^6\)
\(=2^{13}\cdot3^6\)