\(\left(a\right):\dfrac{15x}{7y^3}.\dfrac{2y^2}{x^2}=\dfrac{30}{7xy}\)

\(\left(b\right):\dfrac{x^2-36}{2x+10}.\dfrac{3}{6-x}\\ =\dfrac{\left(x-6\right)\left(x+6\right)}{2x+10}.\dfrac{-3}{x-6}\\ =\dfrac{-3\left(x+6\right)}{2x+10}=\dfrac{-3x-18}{2x+10}\)

\(\left(c\right):\dfrac{1-x^2}{x^2-2x}:\dfrac{x+1}{x}\\ =\dfrac{\left(1-x\right)\left(1+x\right)}{x\left(x-2\right)}.\dfrac{x}{1+x}\\ =\dfrac{1-x}{x-2}\)

\(\left(d\right):\dfrac{1-4x^2}{x^2+4x}:\dfrac{2-4x}{3x}=\dfrac{\left(1-2x\right)\left(1+2x\right)}{x\left(x+4\right)}.\dfrac{3x}{2\left(1-2x\right)}\\ =\dfrac{3\left(1+2x\right)}{2\left(x+4\right)}=\dfrac{3+6x}{2x+8}\)

Có:

\(a^3+b^3+c^3=3abc\\\Leftrightarrow a^3+b^3+c^3-3abc=0\\\Leftrightarrow (a+b)^3+c^3-3ab(a+b)-3abc=0\\\Leftrightarrow (a+b+c)^3-3(a+b)c(a+b+c)-3ab(a+b+c)=0\\\Leftrightarrow (a+b+c)[(a+b+c)^2-3(a+b)c-3ab]=0\\\Leftrightarrow (a+b+c)(a^2+b^2+c^2+2ab+2bc+2ac-3ac-3bc-3ab)=0\\\Leftrightarrow (a+b+c)(a^2+b^2+c^2-ab-bc-ac)=0\\\Leftrightarrow a^2+b^2+c^2-ab-bc-ac=0(vì.a+b+c\ne0)\\\Leftrightarrow 2a^2+2b^2+2c^2-2ab-2bc-2ac=0\\\Leftrightarrow (a^2-2ab+b^2)+(b^2-2bc+c^2)+(a^2-2ac+c^2)=0\\\Leftrightarrow (a-b)^2+(b-c)^2+(a-c)^2=0\)

Ta thấy: \(\left\{{}\begin{matrix}\left(a-b\right)^2\ge0\forall a,b\\\left(b-c\right)^2\ge0\forall b,c\\\left(a-c\right)^2\ge0\forall a,c\end{matrix}\right.\)

\(\Rightarrow\left(a-b\right)^2+\left(b-c\right)^2+\left(a-c\right)^2\ge0\forall a,b,c\)

Mà: \(\left(a-b\right)^2+\left(b-c\right)^2+\left(a-c\right)^2=0\)

nên: \(\left\{{}\begin{matrix}a-b=0\\b-c=0\\a-c=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=b\\b=c\\a=c\end{matrix}\right.\Leftrightarrow a=b=c\)

Thay \(a=b=c\) vào \(A\), ta được:

\(A=\dfrac{\left(2016+\dfrac{a}{a}\right)+\left(2016+\dfrac{b}{b}\right)+\left(2016+\dfrac{c}{c}\right)}{2017^3}\left(a,b,c\ne0\right)\)

\(=\dfrac{2016+1+2016+1+2016+1}{2017^3}\)

\(=\dfrac{2016\cdot3+1\cdot3}{2017^3}\)

\(=\dfrac{3\cdot\left(2016+1\right)}{2017^3}\)

\(=\dfrac{3}{2017^2}\)

Vậy: ...

1. These sentences have been made up to illustrate how different phrasal verbs based on "do" and "make" are used.
2. Why did Bob make off so quickly when I arrived?
3. We're doing up our kitchen, and we could do with more paint.
4. Buying a house is expensive. We'll have to do without a holiday this year.
5. A new house should make for no holiday.
6. We're doing away with our very old cooker and buying a new one.
7. John sent me a note yesterday, and I can't make out what he's written.
8. We didn't have a map, so we made for the hills hoping to find somewhere to stay.