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c) \(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}=\dfrac{1}{2}\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}\right)\)
\(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{11}-\dfrac{1}{13}\right)=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{13}\right)=\dfrac{1}{2}.\dfrac{10}{39}=\dfrac{5}{39}\)
e) \(\dfrac{1}{5}.\dfrac{4}{7}+\dfrac{3}{7}.\dfrac{1}{5}-\dfrac{1}{5}=\dfrac{1}{5}\left(\dfrac{4}{7}+\dfrac{3}{7}\right)-\dfrac{1}{5}=\dfrac{1}{5}.1-\dfrac{1}{5}=0\)
chúc mừng em, em rất may mắn khi cj thấy bài của em:>
Tham khảo nè:
k: \(\left(4x-16\right)\left(-72+9x\right)=0\)
=>\(4\cdot\left(x-4\right)\cdot9\left(x-8\right)=0\)
=>\(36\left(x-4\right)\left(x-8\right)=0\)
=>\(\left(x-4\right)\left(x-8\right)=0\)
=>\(\left[{}\begin{matrix}x-4=0\\x-8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=8\end{matrix}\right.\)
m: \(\left(20+5x\right)\left(4x-8\right)=0\)
=>\(5\cdot\left(x+4\right)\cdot4\left(x-2\right)=0\)
=>\(\left(x+4\right)\left(x-2\right)=0\)
=>\(\left[{}\begin{matrix}x+4=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=2\end{matrix}\right.\)
n: \(\left(-4x+48\right)\left(2x-24\right)=0\)
=>\(-4\left(x-12\right)\cdot2\left(x-12\right)=0\)
=>\(\left(x-12\right)^2=0\)
=>x-12=0
=>x=12
o: \(\left(4x+16\right)\left(-2x+20\right)\left(-40+x\right)=0\)
=>\(4\cdot\left(x+4\right)\cdot\left(-2\right)\left(x-10\right)\left(x-40\right)=0\)
=>\(\left(x+4\right)\left(x-10\right)\left(x-40\right)=0\)
=>\(\left[{}\begin{matrix}x+4=0\\x-10=0\\x-40=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=10\\x=40\end{matrix}\right.\)
p: \(\left(-5x+40\right)\left(-x+2023\right)\left(2x-2\right)=0\)
=>\(-5\left(x-8\right)\cdot\left(-1\right)\cdot\left(x-2023\right)\cdot2\left(x-1\right)=0\)
=>\(\left(x-8\right)\left(x-2023\right)\left(x-1\right)=0\)
=>\(\left[{}\begin{matrix}x-8=0\\x-1=0\\x-2023=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=1\\x=2023\end{matrix}\right.\)
q: \(2024x\left(4x-8\right)\left(5+5x\right)=0\)
=>\(x\cdot4\left(x-2\right)\cdot5\left(x+1\right)=0\)
=>\(x\left(x-2\right)\left(x+1\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x-2=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-1\end{matrix}\right.\)
r: \(-4x\left(3x+9\right)\left(2x-16\right)=0\)
=>\(-4x\cdot3\left(x+3\right)\cdot2\left(x-8\right)=0\)
=>\(x\left(x+3\right)\left(x-8\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x+3=0\\x-8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\\x=8\end{matrix}\right.\)
s: \(\left(-100+5x\right)\left(2x-10\right)\left(6x+6\right)=0\)
=>\(5\cdot\left(x-20\right)\cdot2\left(x-5\right)\cdot6\left(x+1\right)=0\)
=>\(\left(x-20\right)\left(x-5\right)\left(x+1\right)=0\)
=>\(\left[{}\begin{matrix}x-20=0\\x-5=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=20\\x=5\\x=-1\end{matrix}\right.\)
t: \(\left(-2x+4\right)\left(2x+16\right)\cdot\left(7-x\right)=0\)
=>\(-2\left(x-2\right)\cdot2\left(x+8\right)\cdot\left(-1\right)\cdot\left(x-7\right)=0\)
=>\(\left(x-2\right)\left(x+8\right)\left(x-7\right)=0\)
=>\(\left[{}\begin{matrix}x-2=0\\x-7=0\\x+8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-8\\x=7\end{matrix}\right.\)
x : 3 dư 2
x : 5 dư 1
→ x + 4 chia hết cho 3 và 5
→ x + 4 € BC ( 3, 5 )
Ta có: 3 . 5 = 15
→ BC ( 3, 5 ) = B ( 15 ) = {0;15;30;45;...}
Dựa vào các điều kiện trên, ta kết luận: Vậy x € { 15;30 }