\(\frac{3x+1}{\left(x+1\right)^3}=\frac{a}{\left(x+1\right)^3}+\frac{b.\left(x+1\right)}{\left(x+1\right)^3}=\frac{bx+a+b}{\left(x+1\right)^3}\)
=>b = 3
=> a+b =1=> a= 1-b=1-3=-2
Vậy a = -2 ; b = 3
\(\frac{3x+1}{\left(x+1\right)^3}=\frac{a}{\left(x+1\right)^3}+\frac{b.\left(x+1\right)}{\left(x+1\right)^3}=\frac{bx+a+b}{\left(x+1\right)^3}\)
=>b = 3
=> a+b =1=> a= 1-b=1-3=-2
Vậy a = -2 ; b = 3
Xác định các số a, b biết:
\(\frac{\left(3x+1\right)}{\left(x+1\right)^3}\)=\(\frac{a}{\left(x+1\right)^3}\)+\(\frac{b}{\left(x+1\right)^2}\)
\(\text{xác định các số a,b biết :}\)
\(\frac{3x+1}{\left(x+1\right)^3}=\frac{a}{\left(x+1\right)^3}+\frac{b}{\left(x+1\right)^2}\)
Xác định các số a,b biết: \(\frac{3x+1}{\left(x+1\right)^3}\)= \(\frac{a}{\left(x+1\right)^3}\)+ \(\frac{b}{\left(x+1\right)^2}\)
Cho biểu thức: Q= \([\left(x^4-x+\frac{x-3}{x^3+1}\right).\frac{\left(x^3-2x^2+2x-1\right).\left(x+1\right)}{x^9+x^7-3x^2-3}+1-\frac{2\left(x+6\right)}{x^2+1}]\)
a, Tìm điều kiện xác định của biểu thức
b, Rút gọn Q
c, Chứng minh rằng với các giá trị của x thỏa mãn điều kiện xác định thì -5 <= Q <= 0
xác định a,b,c biệt :
a/ \(\frac{9x^2-16x+4}{x^3-3x^2+2x}=\frac{a}{x}+\frac{b}{x-1}+\frac{c}{x-2}\)
b/ \(\frac{1}{\left(x-1\right)^2\left(x-2\right)}=\frac{a}{x-1}+\frac{b}{\left(x-1\right)^2}+\frac{c}{x-2}\)
Tìm các số A , B , C để có
a) \(\frac{x^2-x+2}{\left(x-1\right)^3}=\frac{A}{\left(x-1\right)^3}+\frac{B}{\left(x-1\right)^2}+\frac{C}{x-1}\)
b) \(\frac{x^2+2x-1}{\left(x-1\right)\left(x^2+1\right)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+1}\)
1)\(\frac{1}{\left(a-b\right)\left(a-c\right)}+\frac{1}{\left(b-c\right)\left(b-a\right)}+\frac{1}{\left(c-a\right)\left(c-b\right)}\)
2)\(\frac{a^2}{\left(a-b\right)\left(a-c\right)}+\frac{b^2}{\left(b-c\right)\left(b-a\right)}\frac{c^2}{\left(c-a\right)\left(c-b\right)}\)
3)\(\frac{1}{x^2+3x+2}+\frac{2x}{x^3+4x^2+4x}+\frac{1}{x^2+5x+6}\)
tính(rút gọn)
a,\(\left(x+3-\frac{1}{x+3}\right)\left(x+\frac{3}{x+4}\right)\)
b,\(\left(2x-4-\frac{x-12}{3x+4}\right)\left(3x-2-\frac{10}{2x+1}\right)\)
c,\(\left(2x-8-\frac{x+10}{3x+1}\right)\left(x-6-\frac{x-6}{3x+2}\right)\)
d,\(\left(1+\frac{1}{x}\right):\left(1-\frac{1}{x^2}\right)\)
Giải các phương trình:
a) \(\frac{1}{x-1}-\frac{3x^2}{x^3-1}=\frac{2x}{x^2+x+1}\)
b) \(\frac{3}{\left(x-1\right)\left(x-2\right)}+\frac{2}{\left(x-3\right)\left(x-1\right)}=\frac{1}{\left(x-2\right)\left(x-3\right)}\)
c) \(1+\frac{1}{x+2}=\frac{12}{8+x^3}\)
d) \(\frac{13}{\left(x-3\right)\left(2x+7\right)}+\frac{1}{2x+7}=\frac{6}{\left(x-3\right)\left(x+3\right)}\)