ta có:
\(\frac{1}{\left(x+2\right)\left(x+3\right)}+\frac{1}{\left(x+3\right)\left(x+4\right)}\)
=\(\frac{1}{x+2}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+4}\)
=\(\frac{1}{x+2}-\frac{1}{x+4}\)
=\(\frac{x+4}{\left(x+2\right)\left(x+4\right)}-\frac{x+2}{\left(x+2\right)\left(x+4\right)}\)
\(\frac{2}{\left(x+2\right)\left(x+4\right)}\)
tính (x-2)(x^2+2x+4)-(2+x)(4-2x+x^2)
(2x+1)^2-(4-x)-(5+x)(2-x)+(2+x)^3
(x-1)^3-(x+1)^3+6(x+1)(x-1)
giải phương trình sau:
a) 1/x-2 +3=3-x/x-2
b) x+5/x-5-x-5/x+5=20/x^2-25
c) x/2(x-3) + x/2(x+1)=2x/(x+1)(x-3)
d) 3/5x-1+2/3-5x=4/(1-5x)(x-3)
giải các phươngtrình
1. x3+3x2+x+3 = 0
2. (x2+x+1)(x2+x+2) = 2
3. (2x2+3x-1)2-5(2x2+3x+3)+24=0
4 (x2-4)(x+3)=(x2-4)(x-1)
1) tính
a) \(\frac{4}{x+2}+\frac{3}{2-x}+\frac{12}{x^2-4}\)
b) \(x+\frac{x-1}{2}+\frac{x-2}{3}\)
c) \(\frac{1}{3x-2}-\frac{4}{3x+2}-\frac{3x-6}{4-9x^2}\)
d) x - 2 - \(\frac{x^2-10}{x+2}\)
e) \(\frac{1}{2x-2y}-\frac{1}{2x+2y}+\frac{y}{y^2-x^2}\)
f) \(\frac{1}{a+1}-\frac{3}{a^3+1}+\frac{3}{a^2-a+1}\)
g) \(\frac{4-2x+x^2}{x+2}-2-x\)
h)\(\frac{1}{x^3-x}-\frac{1}{x^2-x}+\frac{2}{x^2-1}\)
j) \(\frac{1}{2x+3}-\frac{1}{2x-3}+\frac{x-2}{2x^2-x-3}\)
1, GIAI CAC PHUONG TRINH SAU
a, (1-x)(5x+3)= (3x-8)(1-x)
b, (x-3)(x+4)-2(3x-2)=(x-4)^2
c,x^2+ x^3+x+1=0
d, (x-3)tren x+3 -2 tren x-3 = 3x+1 tren 9-x^2
(tren co nghia la phan so nha moi nguoi)
(GIIUP EM VOI MN)
Chứng minh đẳng thức:
a.\(\frac{a^3-4a^2-a+4}{a^3-7a^2+14a-8}=\frac{a+1}{a+2}\)
b.\(\frac{x^4+x^3+x+1}{x^4-x^3+2x^2-x+1}=\frac{\left(x+1\right)^2}{x^2+1}\)
giải các phương trình
1) x-\(\dfrac{x-1}{3}+\dfrac{x+2}{6}>\dfrac{2x}{5}+5\)
2)\(\dfrac{2x+6}{6}-\dfrac{x-2}{9}< 1\)
3)\(\dfrac{2x-5}{6}< \dfrac{4+3x}{9}\)
4) \(5+\dfrac{x+4}{5}< x-\dfrac{x-2}{2}+\dfrac{x+3}{3}\))
5) \(x+1-\dfrac{x-1}{3}< \dfrac{2x+3}{2}+\dfrac{x}{3}+5\)
6) \(\dfrac{2x-3}{4}-\dfrac{x+1}{3}>\left(-\right)\dfrac{1}{2}-\dfrac{3-x}{5}\)
Bài 1: đã biết x^3 -y^3=(x-y)*(x^2+xy+y^2)
a/ chứng minh (x^5 -1)= (x-1)*(x^4+x^3+x^2+x+1)
b/ Suy ra tổng quát : X^n -1=? ( n lẻ)
Bài 2 : Viết tổng sau thành tích :
a/ x^2 +2xy+y^2-4
b/ 4x^2-y^2-4y-4
c/25a^4-x^2+4xy-4y^2
Giải pt:
a)(x^2-1)(x^2+4x+3)=192
b)x^5-x^4+3x^3+3x^2-x+1)=0
c)x^4+3x^3+4x^2+3x+1=0
bài 1: tính
A=4^2−3x+17/x^3−1 +2x−1/x^2+x+1 +6/1−x
B=3x+1/x^2−2x+1 −1/x+1 +x+3/1−x2
C=(x/x+1 +1):(1−3x^2/1−x^2 )
D=(x^2/y^2 +y/x ):(x/y^2 −1/y +1/x )
E=(1/x^2+4x+4 −1/x^2−4x+4 ):(1/x+2 +1/x−2 )
F=1/x−1 −x^3−x/x^2+1 (1/x^2−2x+1 +1/1−x^2 )
