\(\frac{1}{9}\).27n = 3n +2
\(\frac{1}{9}\).34 . 3n = 37
\(\frac{1}{2}\). 4n + 4.4n = 9 . 2n + 1
\(\frac{3x}{5x+5y}-\frac{x}{10x-10y}\\ \left(\frac{3x}{1-3n}+\frac{2n}{3x+1}\right):\left(\frac{6x^2+10x}{1-6x+9x^2}\right)\\ \left(\frac{9}{x^3-9n}+\frac{1}{x+3}\right):\left(\frac{x}{3n+9}\right)\)
\(\frac{3x}{5x+5y}-\frac{x}{10x-10y}\)
= \(\frac{3x\left(x-y\right)}{5.2.\left(x+y\right)\left(x-y\right)}-\frac{x\left(x+y\right)}{10\left(x^2-y^2\right)}\)
= \(\frac{3x^2-3xy-x^2-xy}{10\left(x^2-y^2\right)}\)
= \(\frac{3x\left(x-y\right)}{10\left(x^2-y^2\right)}\)
= \(\frac{3x}{10\left(x+y\right)}\)
\(\frac{4n+1}{3n+2}\)
\(\frac{3n^2-2n+5}{3n-2}\)
7n + 1 chia hết cho 3n -2
-4n + 5 chia hết cho 2n -1
CMR: với số nguyên dương \(n\ge2\) ta có \(\frac{2n+1}{3n+2}< \frac{1}{2n+2}+\frac{1}{2n+3}+...+\frac{1}{4n+2}< \frac{3n+2}{4\left(n+1\right)}\)
Tìm n để biểu thức sau là số nguyên :
\(A=\frac{2n+1}{n+2}-\frac{n+1}{n+2}+\frac{3n+5}{2n+4}+\frac{4n+6}{3n+6}-\frac{10n+12}{5n+10}-\frac{12n+3}{4n+8}\)
CMR: với mọi số nguyên dương \(n\ge2\) ta có \(\frac{2n+1}{3n+2}< \frac{1}{2n+2}+\frac{1}{2n+3}+...+\frac{1}{4n+2}< \frac{3n+2}{4\left(n+1\right)}\)
Tôi cũng là của FC Real Madrid ở Hà Nam.
Chúng mình kết bạn nhé.hihi.
tim n thuoc Z để các phân số sau nguyên:
a) \(\frac{3n-1}{4n+5}\)
b) \(\frac{2n+9}{n+2}\) - \(\frac{3n}{n+2}\) + \(\frac{5n+17}{n+2}\)
Tính:
\(\frac{4n+3}{7n+1}-\frac{3n-2}{7n+1}+\frac{2n-3}{7n+1}.\)
Đặt \(A=\frac{4n+3}{7n+1}-\frac{3n-2}{7n+1}+\frac{2n-3}{7n+1}\) ta có :
\(A=\frac{4n+3-3n+2+2n-3}{7n+1}\)
\(A=\frac{3n+2}{7n+1}\)
Vậy \(A=\frac{3n+2}{7n+1}\)
Chúc bạn học tốt ~
(4n+3-(3n-2)+(2n-3))/7n+1
(4n+3-3n+2+2n-3)/7n+1
=(3n-2)/7n+1
lim \(\frac{\left(2n^2-3n+5\right)\left(2n+1\right)}{\left(4-3n\right)\left(2n^2+n+1\right)}\)
lim \(\frac{\sqrt{n^4+1}}{n}-\frac{\sqrt{4n^6+2}}{n^2}\)
lim \(\frac{2n+3}{\sqrt{9n^2+3}-\sqrt[3]{2n^2-8n^3}}\)
a) lim \(\frac{\left(2n^2-3n+5\right)\left(2n+1\right)}{\left(4-3n\right)\left(2n^2+n+1\right)}\)
= lim \(\frac{\left(2-\frac{3}{n}+\frac{5}{n^2}\right)\left(2+\frac{1}{n}\right)}{\left(\frac{4}{n}-3\right)\left(2+\frac{1}{n}+\frac{1}{n^2}\right)}=\frac{4}{-6}=-\frac{2}{3}\)
b)lim ( \(\frac{\sqrt{n^4+1}}{n}-\frac{\sqrt{4n^6+2}}{n^2}\))
= lim ( \(\frac{n\sqrt{n^4+1}-\sqrt{4n^6+2}}{n^2}\) )
= lim \(\frac{\left(n^6+n^2\right)-\left(4n^6+2\right)}{n^2\left(n\sqrt{n^4+1}+\sqrt{4n^2+2}\right)}\)
= lim \(\frac{-3n^6+n^2+2}{n^3\sqrt{n^4+1}+n^2\sqrt{4n^2+2}}\)
= lim \(\frac{-3n\left(1-\frac{1}{n^4}-\frac{2}{n^6}\right)}{\sqrt{1+\frac{1}{n^4}}+\frac{1}{n^2}\sqrt{4+\frac{2}{n^2}}}\)
= lim \(-3n=-\infty\)
c) lim \(\frac{2n+3}{\sqrt{9n^2+3}-\sqrt[3]{2n^2-8n^3}}\)
= lim\(\frac{2+\frac{3}{n}}{\sqrt{9+\frac{3}{n^2}}-\sqrt[3]{\frac{2}{n}-8}}=\frac{2}{3+2}=\frac{2}{5}\)
A= \(\frac{5n+17}{n+3}+\frac{-3n}{n+3}+\frac{2n+9}{n+3}+\frac{-4n-23}{n+3}\)
\(A=\frac{5n+17}{n+3}+\frac{-3n}{2+3}+\frac{2n+9}{n+3}+\frac{-4n-23}{n+3}\)
\(=\frac{5n+17-3n+2n+9-4n-23}{n+3}\)
\(=\frac{3}{n+3}\)
1. Rút gọn :
a) \(\frac{8^6.25^5}{16^5.125^3}\) b) \(\frac{9^3.5-3^6.2}{9^4+3^8.5}\)
2. Phân số \(\frac{3n+2}{4n-5}\) có thể rút gọn cho số nào ?
3. CMR : \(\frac{3n-1}{2n-1}\) là phân số tối giản ( n \(\in\) Z )
Ai có thể giúp mìk zới !!! :">