\(\dfrac{4}{21}+\dfrac{-5}{8}+\dfrac{17}{21}+\dfrac{-3}{8}\\ =\left(\dfrac{4}{21}+\dfrac{17}{21}\right)+\left(-\dfrac{5}{8}-\dfrac{3}{8}\right)\\ =\dfrac{21}{21}+\dfrac{-8}{8}=1-1=0\)

\(ĐK:\)\(a>0;a\ne1\)

\(A=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{a-\sqrt{a}}\right):\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{2}{a-1}\right)\\ =\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\right):\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\\ =\dfrac{\sqrt{a}^2-1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\dfrac{\sqrt{a}-1+2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\\ =\dfrac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)}.\dfrac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{\sqrt{a}+1}=\dfrac{a-1}{\sqrt{a}}\)

\(a\\ 64^2+36^2+2.64.36=\left(64+36\right)^2=100^2=10000\\ b\\ 64^2+36^2-2.64.36=\left(64-36\right)^2=28^2=784\)

\(\left(x+0,7\right)^3=-27=\left(-3\right)^3\\ =>x+0,7=-3\\ =>x=-3-0,7=-3,7\)

\(\left(2x-1\right)^{10}=49^5=\left(7^2\right)^5=7^{2.5}\\ =>\left(2x-1\right)^{10}=7^{10}=\left(\pm7\right)^{10}\\ =>\left[{}\begin{matrix}2x-1=7\\2x-1=-7\end{matrix}\right.=>\left[{}\begin{matrix}x=4\\x=-3\end{matrix}\right.\)

\(2x-1=4x+3\\ =>4x-2x=-3-1\\ =>2x=-4\\ =>x=-2\)

\(Cùng\ chia\ cả\ tử\ và\ mẫu\ cho\ 3x4x5x...x100\, \ ta\ được :\)

\(\dfrac{1x2x3x4x5x...x101}{3x4x5x6x...x100}=2x101=202\)

\(ĐK:n\in Z;n\ne-4\)

\(B=\dfrac{2n+9}{n+4}=\dfrac{2\left(n+4\right)+1}{n+4}=2+\dfrac{1}{n+4}\)

\(Để\ B\ là \ số \ nguyên\ thì :\) \(\dfrac{1}{n+4}\in Z=>1⋮\left(n+4\right)\\ =>n+4\inƯ\left(1\right)=\left\{\pm1\right\}=>n\in\left\{-5;-3\right\}\left(TMDK\right)\)

\(\left(\dfrac{4}{5}\right)^5.x=\left(\dfrac{4}{5}\right)^7\\ =>x=\left(\dfrac{4}{5}\right)^7:\left(\dfrac{4}{5}\right)^5=\left(\dfrac{4}{5}\right)^{7-5}=\left(\dfrac{4}{5}\right)^2\\ =>x=\dfrac{16}{25}\)

\(\dfrac{1}{4}+\dfrac{3}{4}x=-3\dfrac{1}{2}\\ =>\dfrac{3}{4}x=\dfrac{\left(-3\right)\times2+1}{2}-\dfrac{1}{4}\\ =>\dfrac{3}{4}x=-\dfrac{5}{2}-\dfrac{1}{4}\\ =>\dfrac{3}{4}x=\dfrac{-10-1}{4}=-\dfrac{11}{4}\\ =>x=-\dfrac{11}{4}:\dfrac{3}{4}=-\dfrac{11}{3}\)