`a)`

`(x^4 + 12x^2 -5x):(-x)`

`=[x^4 : (-x)] + [12x^2 : (-x)] - [5x:(-x)]`

`=-x^3 - 12x + 5`

`b)`

`(15 x^5 y^9 - 10 x^3 y^5 + 25 x^4 y^4) : 5x^2 y^2`

`=(15 x^5 y^9 : 5 x^2 y^2) - (10 x^3 y^5 : 5x^2 y^2) + (25 x^4 y^4 : 5 x^2 y^2)`

`=3 x^3 y^7 - 2 x y^3 + 5 x^2 y^2`

\(\sqrt{5^2-4^2}=\sqrt{25-16}=\sqrt{9}=3\)

\(\left(a\right)x⋮9\) và \(18< x\le36\)

\(x\in B\left(9\right)\) và \(18< x\le36\)

\(B\left(9\right)=\left\{0;9;18;27;36;45;...\right\}\)

Vậy \(x=27\) hoặc \(x=36\)

\(\left(b\right)\)

\(24=2^3.3\)

\(30=2.3.5\)

\(BCNN\left(24;30\right)=2^3.3.5=120\)

\(\left(c\right)140⋮x,84⋮x\) và \(x>9\)

\(\Rightarrow x\inƯC\left(140;84\right)\) và \(x>9\)

\(140=2^2.5.7\)

\(84=2^2.3.7\)

\(ƯCLN\left(140;84\right)=2^2.7=28\)

\(ƯC\left(140;84\right)=Ư\left(28\right)=\left\{1;2;4;7;14;28\right\}\)

\(x\inƯC\left(140;84\right)\) và \(x>9\) nên \(x=14\) hoặc \(x=28\)

\(\left|9+x\right|=­2x\)

\(\left|9+x\right|-2x=0\)

\(\left\{{}\begin{matrix}x=9,x\ge-9\\x=-3,x< -9\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x=9\\\varnothing\end{matrix}\right.\)

\(x=9\)

\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}=\dfrac{8}{24}+\dfrac{4}{24}+\dfrac{2}{24}+\dfrac{1}{24}=\dfrac{8+4+2+1}{24}=\dfrac{15}{24}=\dfrac{5}{8}\)

Số học sinh khá của lớp 3A là :

\(15\times2=30\left(hs\right)\)

\(3.2^x=96\)

\(2^x=96:3\)

\(2^x=32\)

\(2^x=2^5\)

\(x=5\)

\(a,\dfrac{4}{9};\dfrac{17}{13};\dfrac{33}{77}\)

\(b,\dfrac{12}{21};\dfrac{36}{63};\dfrac{56}{24}\)