rút gọn :
a,\(\frac{x^5y}{\left(xy^4\right)}\)
b, \(\frac{3\times x^2\times y^5}{9\times x\times y^4}\)
c, \(\frac{\left(3\times x\times y^2\right)^4}{27\times x^5y^3}\)
cho \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=2\)và \(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=2\)
chứng minh \(a+b+c=a\times b\times c\)
tìm x , biết :
\(\frac{4}{5}x^2\times\left(\frac{x}{3}-\frac{1}{2}\right)-\left(\frac{1}{5}x-\frac{2}{3}\right)\times\left(\frac{4x^2}{3}+1\right)=\frac{22}{45}x^2\)
cho \(a+b+c=a\times b\times c\)
\(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=2\)
tính \(M=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)
Tính nhanh :
a ) S = 2+4+6+8+.....+2018
b ) S= 10+102+103+...+10100
c) \(S=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{100}}\)
d) \(S=\frac{1!}{3!}+\frac{2!}{4!}+\frac{3!}{5!}+....+\frac{2018!}{2020!}\)
biết rằng : \(n!=1\times2\times3\times...\times n\)
VD : 1! = 1
2! = 2.1
3!=1.2.3
4!=1.2.3.4
! : giai thừa
A=\(\left(\frac{4x}{x+2}-\frac{x^3-8}{x^3+8}\times\frac{4x^2-8x+16}{x^2-4}\right)\)) : \(\frac{16}{x+2}\times\frac{x^2+3x+2}{x^2+x+1}\)
a)rút gọn A
b) vs gt nào của x thì A+B có gt Max. Tìm gt lớn nhất đó
Rút gọn biểu thức
\(\frac{x^7+3x^2+2}{x^3-1}\times\frac{3x}{x+1}\times\frac{x^2+x+1}{x^7+3x^2+2}\)
Cho
P=\(\left(\frac{2}{\left(x+1\right)^3}\times\left(\frac{1}{x}+1\right)+\frac{1}{x^2+2x+1}\times\left(\frac{1}{x^2}+1\right)\right)\div\frac{x-1}{x^3}\)
a) Rút gọn P
b)Tìm x để P<1
c)Tìm x thuộc Z để P thuộc Z
Rút gọn \(B=\left(x^4-x+\frac{x-3}{x^3+1}\times\frac{\left(x^3-2x^2+2x-1\right)\left(x+1\right)}{x^9+x^7-3x^2-3}+1-\frac{2\left(x+6\right)}{x^2+1}\right)\times\frac{4x^2+6x+1}{\left(x+3\right)\left(4-x\right)}\)