Rút gọn biểu thức
\(A=\dfrac{1^4+4}{3^4+4}+\dfrac{5^4+4}{7^4+4}+\dfrac{9^4+4}{11^4+4}+\dfrac{13^4+4}{15^4+4}+\dfrac{17^4+4}{19^4+4}\)
Giải phương trình :
a)\(\dfrac{3x-2}{5}+\dfrac{x-1}{9}=\dfrac{14x-3}{15}-\dfrac{2x+1}{9}\)
b)\(\dfrac{x+3}{2}-\dfrac{2-x}{3}-1=\dfrac{x+5}{6}\)
c)\(\dfrac{x+5}{2010}+\dfrac{x+4}{2011}+\dfrac{x+3}{2012}+\dfrac{x+2}{2013}=-4\)
d)\(\dfrac{x-12}{77}+\dfrac{x-11}{78}=\dfrac{x-74}{15}+\dfrac{x-72}{16}\)
thực hiện phép tính:
1) \(\dfrac{-1}{12}\)- (2\(\dfrac{5}{8}\)- \(\dfrac{1}{3}\))
2) -1,75 - (\(\dfrac{-1}{9}\) - 2\(\dfrac{1}{18}\))
3) -\(\dfrac{5}{6}\) - (\(-\dfrac{3}{8}\)+\(\dfrac{1}{10}\))
4) \(\dfrac{2}{5}\)+(\(-\dfrac{4}{3}\))+(\(-\dfrac{1}{2}\))
5) \(\dfrac{3}{12}\)- (\(\dfrac{6}{15}\)- \(\dfrac{3}{10}\))
6) (\(8\dfrac{5}{11}\)+\(3\dfrac{5}{8}\))- \(3\dfrac{5}{11}\)
7) \(\dfrac{-1}{4}\). \(13\dfrac{9}{11}\)- 0,25 . \(6\dfrac{2}{11}\)
8) \(\dfrac{4}{9}\):(\(-\dfrac{1}{7}\))+ \(6\dfrac{5}{9}\): (\(-\dfrac{1}{7}\))
Cho bài toán sau: \(\left(1-\dfrac{2}{5}\right).\left(1-\dfrac{2}{7}\right).\left(1-\dfrac{2}{9}\right).\left(1-\dfrac{2}{11}\right).....\left(1-\dfrac{2}{113}\right)=\dfrac{a}{b}\)khi đó a+b = ?
Biểu diễn \(B=27+\dfrac{27}{15+\dfrac{7}{2008}}\) dưới dạng \(B=K_0+\dfrac{1}{K_1+\dfrac{1}{K_2+\dfrac{1}{...+\dfrac{1}{K_n-1+\dfrac{1}{K_n}}}}}\)
Một số bài toán máy tính cầm tay.
Tính:
a, \(\dfrac{1}{3}-\dfrac{3}{4}-\left(-\dfrac{3}{5}\right)+\dfrac{1}{64}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{15}\)
b, \(\left(3-\dfrac{1}{4}+\dfrac{2}{3}\right)-\left(5-\dfrac{1}{3}-\dfrac{6}{5}\right)-\left(6-\dfrac{7}{4}-\dfrac{3}{2}\right)\)
CMR \(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+...+\dfrac{1}{19}< 2\)
Bài 1: Tìm x:
a) \(\left|x+\dfrac{4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\)
b) \(\left|\dfrac{5}{3}x\right|=\left|-\dfrac{1}{6}\right|\)
c) \(\left|\dfrac{3}{4}x-\dfrac{3}{4}\right|-\dfrac{3}{4}=\left|-\dfrac{3}{4}\right|\)
Bài 2: Tìm x,y:
a) \(\left|\dfrac{1}{2}-\dfrac{1}{3}+x\right|=\dfrac{1}{4}-\left|y\right|\)
b) \(\left|x-y\right|+\left|y+\dfrac{9}{25}\right|=0\)
Bài 3: Tìm giá trị nhỏ nhất:
a) A= \(\left|x+\dfrac{15}{19}\right|-1\)
b) B= \(\dfrac{1}{2}+\left|x-\dfrac{4}{7}\right|\)
Bài 4: Tìm giá trị lớn nhất:
a) A= 5- \(\left|\dfrac{5}{3}-x\right|\)
b) B= 9-\(\left|x-\dfrac{1}{10}\right|\)
Giải phương trình sau:
\(\dfrac{2x-1}{5}-\dfrac{x-2}{3}=\dfrac{x+7}{15}\)
\(\dfrac{5x+2}{6}-\dfrac{8x-1}{3}=\dfrac{4x+2}{5}-5\)