Tìm số tự nhiên x để phân số x thuộc số tự nhiên
x+1/x-7
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\(a,\dfrac{x}{15}=2\dfrac{2}{3}=\dfrac{8}{3}\Rightarrow x=\dfrac{15\cdot8}{3}=40\\ b,\dfrac{108}{x}=1\dfrac{4}{5}=\dfrac{9}{5}\Rightarrow x=\dfrac{108\cdot5}{9}=60\\ c,\dfrac{x}{2}< 1\dfrac{1}{2}\Rightarrow\dfrac{x}{2}=\dfrac{3}{2}\Rightarrow x< 3\)
Ta có: \(11=11;220=2^2\cdot5\cdot11;55=5\cdot11\)
=>BCNN(11;220;55)=\(2^2\cdot5\cdot11=220\)
x⋮11; x⋮220; x⋮55
=>x∈BC(11;220;55)
=>x∈B(220)
=>x=220k(k∈N)
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Ta có:
\(\frac{x+1}{x-7}=\frac{x-7+8}{x-7}=1+\frac{8}{x-7}\)
Để phân số trên là số tự nhiên thì: \(\frac{8}{x-7}\)là số tự nhiên
hay\(8⋮\left(x-7\right)\Rightarrow x-7\inƯ\left(8\right)\Rightarrow x-7\in\left(1;2;4;8\right)\)
\(\Rightarrow x\in\left(8;9;11;15\right)\)
Vậy................................ Chúc bn hok tốt !!
day la toan ma