Violympic toán 8
Các câu hỏi tương tự
1. a, tính gt nhỏ nhất của biểu thức
Afrac{2x^2-16x+41}{x^2-8x+22}
b, tính gt lớn nhất của biểu thúc
Bfrac{3x^2+9x+17}{3x^2+9x+7}
2. cho bt Qleft[left(x^4-x+frac{x-3}{x^3+1}right).frac{left(x^3-2x^2+2x-1right)left(x+1right)}{x^9+x^7-3x^2-3}+1-frac{2left(x+6right)}{x^2+1}right].frac{4x^2+4x+1}{left(x+3right)left(4-xright)}
Đọc tiếp
1. a, tính gt nhỏ nhất của biểu thức
A=\(\frac{2x^2-16x+41}{x^2-8x+22}\)
b, tính gt lớn nhất của biểu thúc
B=\(\frac{3x^2+9x+17}{3x^2+9x+7}\)
2. cho bt Q=\(\left[\left(x^4-x+\frac{x-3}{x^3+1}\right).\frac{\left(x^3-2x^2+2x-1\right)\left(x+1\right)}{x^9+x^7-3x^2-3}+1-\frac{2\left(x+6\right)}{x^2+1}\right].\frac{4x^2+4x+1}{\left(x+3\right)\left(4-x\right)}\)
rút gọn biểu thức
\(1-\left(\frac{2x^2+x-1}{1-x^2}+\frac{2x^3-x+x^2}{1+x^3}\right):\frac{\left(1-x\right)\left(x^2-x\right)}{2x-1}\)
Giải các phương trình sau
a) frac{1}{x+1}-frac{5}{x-2}frac{15}{left(x+1right)left(2-xright)}
b) frac{1}{2x-3}-frac{3}{xleft(2x-3right)}frac{5}{x}
c) frac{6}{x-1}-frac{4}{x-3}frac{8}{2x-6}
d) frac{3}{left(x-1right)left(x-2right)}+frac{2}{left(x-3right)left(x-1right)}frac{1}{left(x-2right)left(x-3right)}
e) frac{1}{x-2}+frac{5}{x+1}frac{3}{2-x}
f) frac{5x}{2x+2}+1-frac{6}{x+1}
g) frac{x+1}{x-1}-frac{x-1}{x+1}frac{4}{x^2-1}
h) frac{3x}{x-2}-frac{x}{x-5}frac{3x}{left(x-2right)left(5-xright)}
Đọc tiếp
Giải các phương trình sau
a) \(\frac{1}{x+1}-\frac{5}{x-2}=\frac{15}{\left(x+1\right)\left(2-x\right)}\)
b) \(\frac{1}{2x-3}-\frac{3}{x\left(2x-3\right)}=\frac{5}{x}\)
c) \(\frac{6}{x-1}-\frac{4}{x-3}=\frac{8}{2x-6}\)
d) \(\frac{3}{\left(x-1\right)\left(x-2\right)}+\frac{2}{\left(x-3\right)\left(x-1\right)}=\frac{1}{\left(x-2\right)\left(x-3\right)}\)
e) \(\frac{1}{x-2}+\frac{5}{x+1}=\frac{3}{2-x}\)
f) \(\frac{5x}{2x+2}+1=-\frac{6}{x+1}\)
g) \(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{4}{x^2-1}\)
h) \(\frac{3x}{x-2}-\frac{x}{x-5}=\frac{3x}{\left(x-2\right)\left(5-x\right)}\)
3) frac{1-x}{x+1}-frac{3+2x}{x+1}0
13) frac{x+2}{x}-frac{x^2+5x+4}{xleft(x+2right)}frac{x}{x+2}
14) frac{1}{x+1}-frac{5}{x-2}frac{20}{left(x+1right)left(2-xright)}
16) frac{x+5}{x-5}-frac{x-5}{x+5}frac{20}{x^2-25}
17) frac{3x+2}{3x-2}-frac{6}{2+3x}frac{9x^2}{9x^2-4}
18) frac{x-1}{x}+frac{1}{x+1}frac{2x-1}{2x^2+2}
19) frac{2}{x+1}-frac{3x+1}{left(x+1right)}frac{1}{left(x+1right)left(x-2right)}
20) frac{x+5}{3x-6}-frac{1}{2}frac{2x-3}{2x-4}
Đọc tiếp
3) \(\frac{1-x}{x+1}-\frac{3+2x}{x+1}=0\)
13) \(\frac{x+2}{x}-\frac{x^2+5x+4}{x\left(x+2\right)}=\frac{x}{x+2}\)
14) \(\frac{1}{x+1}-\frac{5}{x-2}=\frac{20}{\left(x+1\right)\left(2-x\right)}\)
16) \(\frac{x+5}{x-5}-\frac{x-5}{x+5}=\frac{20}{x^2-25}\)
17) \(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x^2-4}\)
18) \(\frac{x-1}{x}+\frac{1}{x+1}=\frac{2x-1}{2x^2+2}\)
19) \(\frac{2}{x+1}-\frac{3x+1}{\left(x+1\right)}=\frac{1}{\left(x+1\right)\left(x-2\right)}\)
20) \(\frac{x+5}{3x-6}-\frac{1}{2}=\frac{2x-3}{2x-4}\)
Cho biểu thức
A=\(\left[\frac{3\left(x+2\right)}{2\left(x^3+x^2+x+1\right)}+\frac{2x^2-x-10}{2\left(x^3-x^2+x-1\right)}\right]:\left[\frac{5}{x^2+1}+\frac{3}{2\left(x+1\right)}-\frac{3}{2\left(x+1\right)}\right]\)
11 tháng 3 2020 lúc 15:52
a, (x-1)3 - x(x-1)2 = 5(2-x) - 11(x+2)
b, (x-2)3 + (3x-1)(3x+1) = (x+1)3
c, \(\frac{2x-1}{5}-\frac{x-2}{3}=\frac{x+7}{5}\)
d, \(\frac{2\left(x-3\right)}{7}+\frac{x-5}{3}=\frac{13x+4}{21}\)
e, \(\frac{\left(x+10\right)\left(x+4\right)}{12}-\frac{\left(x+4\right)\left(2-x\right)}{4}=\frac{\left(x+10\right)\left(x-2\right)}{3}\)
Giải các bất phương trình sau :
a) \(15-2x\left(1-x\right)< 2x^2-4x+5\)
b) \(x^2-\frac{x\left(3x+2\right)}{3}< \frac{x-6}{3}\)
c) \(1+\frac{x+4}{3}< x-\frac{x-3}{2}\)
d) \(\left(\frac{2x+1}{2}\right)^2+\frac{3x\left(1-x\right)}{3}-\frac{5x}{4}\le1\)
Giải các phương trình sau
a) frac{7x-3}{x-1}frac{2}{3}
b) frac{2left(3-7xright)}{1+x}frac{1}{2}
c) frac{1}{x-2}+3frac{3-x}{x-2}
d) frac{8-x}{x-7}-8frac{1}{x-7}
e) frac{x+5}{x-5}-frac{x-5}{x+5}frac{20}{x^2-25}
f)frac{1}{x-1}+frac{2}{x+1}frac{x}{x^2-1}
g) frac{x}{2left(x-3right)}+frac{x}{2left(x+1right)}frac{2x}{left(x+1right)left(x-3right)}
h)5+frac{76}{x^2-16}frac{2x-1}{x+4}-frac{3x-1}{4-x}
i) frac{90}{x}-frac{36}{x-6}2
k) frac{1}{x}+frac{1}{x10}frac{1}{12}
l) frac{x+3}{x-3}-frac{1}{x...
Đọc tiếp
Giải các phương trình sau
a) \(\frac{7x-3}{x-1}=\frac{2}{3}\)
b) \(\frac{2\left(3-7x\right)}{1+x}=\frac{1}{2}\)
c) \(\frac{1}{x-2}+3=\frac{3-x}{x-2}\)
d) \(\frac{8-x}{x-7}-8=\frac{1}{x-7}\)
e) \(\frac{x+5}{x-5}-\frac{x-5}{x+5}=\frac{20}{x^2-25}\)
f)\(\frac{1}{x-1}+\frac{2}{x+1}=\frac{x}{x^2-1}\)
g) \(\frac{x}{2\left(x-3\right)}+\frac{x}{2\left(x+1\right)}=\frac{2x}{\left(x+1\right)\left(x-3\right)}\)
h)\(5+\frac{76}{x^2-16}=\frac{2x-1}{x+4}-\frac{3x-1}{4-x}\)
i) \(\frac{90}{x}-\frac{36}{x-6}=2\)
k) \(\frac{1}{x}+\frac{1}{x=10}=\frac{1}{12}\)
l) \(\frac{x+3}{x-3}-\frac{1}{x}=\frac{3}{x\left(x-3\right)}\)
m) \(\frac{3}{x+2}-\frac{2}{x-2}+\frac{8}{x^2-4}=0\)
n) \(\frac{3}{x+2}-\frac{2}{x-3}=\frac{8}{\left(x-3\right)\left(x+2\right)}\)
o)\(\frac{x}{2x+6}-\frac{x}{2x+2}=\frac{3x+2}{\left(x+1\right)\left(x+3\right)}\)
p) \(\frac{x}{x+1}-\frac{2x-3}{1-x}=\frac{3x^2+5}{x^2-1}\)
q) \(\frac{5}{x+7}+\frac{8}{2x+14}=\frac{3}{2}\)
r) \(\frac{x-1}{x}=\frac{1}{x+1}=\frac{2x-1}{x^2+x}\)
1 Giari các PT:
a, \(\frac{2}{x+1}-\frac{1}{x-2}=\frac{3x-11}{\left(x-1\right)\left(x-2\right)}\)
b, \(\left(\frac{3}{2x+1}+2\right)\left(5x-2\right)=\frac{5x-2}{2x+1}\)