1. Rút gọn phân số
a)\(\dfrac{57}{77}\) b)\(\dfrac{2.7-8.3}{30}\) c)\(\dfrac{18.27+18.\left(-23\right)}{34.4-4.52}\)
d\(\dfrac{2^5.3^7}{6^4.81}\) e\(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}\) f \(\dfrac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}\)
2.tìm số nguyên x để mỗi phân số sau có giá trị là số nguyên
a)\(\dfrac{26}{x+3}\) b\(\dfrac{x+6}{x+1}\)
3.chứng minh rằng các phân số sau tối giản vs mọi số tự nhiên n
\(\dfrac{n}{6n-1}\) \(\dfrac{n+1}{2n+3}\)
Giúp mik vs ạ cần gấp
\(a,\dfrac{26}{x+3}\in Z.\\ \Leftrightarrow x+3\inƯ\left(26\right)=\left\{1;-1;2;-2;26;-26\right\}.\)
\(TH1:x+3=1.\\ \Leftrightarrow x=-2\left(TM\right).\\ TH2:x+3=-1.\\ \Leftrightarrow x=-4\left(TM\right).\\ TH3:x+3=2.\\ \Leftrightarrow x=-1\left(TM\right).\\ TH4:x+3=-2.\\ \Leftrightarrow x=-5\left(TM\right).\\ TH5:x+3=26.\\ \Leftrightarrow x=23\left(TM\right).\\ \Leftrightarrow TH6:x+3=-26.\\ \Leftrightarrow x=-29\left(TM\right).\)
Vậy \(x\in\left\{-2;-4;-5;23;-29\right\}.\)
\(b,\dfrac{x+6}{x+1}=1+\dfrac{5}{x+1}\left(x\ne-1\right).\\ 1+\dfrac{5}{x+1}\in Z.\\ \Leftrightarrow x+1\inƯ\left(5\right)=\left\{1;-1;-5;5\right\}.\)
\(TH1:x+1=1.\\ \Leftrightarrow x=0\left(TM\right).\\ TH2:x+1=-1.\\ \Leftrightarrow x=-2\left(TM\right).\\ TH3:x+1=5.\\ \Leftrightarrow x=4\left(TM\right).\\ TH4:x+1=-5.\\ \Leftrightarrow x=-6\left(TM\right).\)
Vậy \(x\in\left\{0;-2;4;-6\right\}.\)
