1. \(\frac{x-1}{x}+\frac{x-2}{x+1}=2\) (1)
ĐKXĐ: x≠0; x≠-1
(1)⇒(x-1)(x+1)+x(x-2)=2x(x+1)
⇔ 2x2-2x-1=2x2+2x
⇔ 2x2-2x2-2x-2x=1
⇔ -4x=1
⇔ x=\(\frac{-1}{4}\)(tmđk)
Vậy x=\(\frac{-1}{4}\) là nghiệm của phương trình
2. \(\frac{x}{x-1}+\frac{x-1}{x}=2\) (2)
ĐKXĐ: x≠0; x≠1
(2)⇒ x2+(x-1)2=2x(x-1)
⇔ 2x2-2x+1=2x2-2x
⇔ 2x2-2x2-2x+2x=-1
⇔ 0x=-1
⇔ x ∈ ∅
Vậy phương trình đã cho vô nghiệm
Tìm x biết : 6(x+2)(x-3)-3(x-2)^2-3(x-1)(x+1)=1
3(x+2)^2+(2x-1)^2-7(x+3)(x-3)=36
(x-1)(x^2+x+1)+x(x+2)(2-x)=5
(x-1)^3-(x+3)(x^2-3x+9)+3(x^2-4)=2
Tìm x biết : 6(x+2)(x-3)-3(x-2)^2-3(x-1)(x+1)=1
3(x+2)^2+(2x-1)^2-7(x+3)(x-3)=36
(x-1)(x^2+x+1)+x(x+2)(2-x)=5
(x-1)^3-(x+3)(x^2-3x+9)+3(x^2-4)=2
tìm x:
a) (x-5)(x+5)-(x-2)^2-7x^2+(x+1)(x^2-x+1)=(x+3)^3-(x^3+9x^2)
b) (2x+3)^2+(x-1)(x+1)=5(x+2)^2-(x-5)(x+1)+(x+4)^2
(x+1)/(x^2+x+1) - (x-1)/(x^2-x-1) = [2.(x+2)^2]/(x^6-1)
giải pt
1,\(\frac{1}{x-1}+\frac{2x^2-5}{x^3-1}=\frac{4}{x^2+x+1}\)
2,\(\frac{x+4}{2x^2-5x+2}+\frac{x+1}{2x^2-7x+3}=\frac{2x+5}{2x^2-7x+3}\)
3,\(\frac{x+1}{x-1}-\frac{x-1}{x+1}=3x\left(1-\frac{x-1}{x+1}\right)\)
4,\(\frac{2x}{x-1}+\frac{4}{x^2+2x-3=}=\frac{2x-5}{x+3}\)
5,\(\frac{1}{x-1}-\frac{7}{x+2}=\frac{3}{x^2+x-2}\)
6,\(\frac{x+3}{x-4}+\frac{x-1}{x-2}=\frac{2}{6x-8-x^2}\)
7,\(\frac{1}{x-1}-\frac{7}{x+2}=\frac{3}{1-x^2}\)
Giải pt x+1/x^2+x+1 -x-1/x^2-x+1=3/x(x^4+x^2+1)
a) -3x(x+2)²+(x+3)(x-1)(x+1)-(2x-5)²
b) 2(x-3)(x+3)(x+2)-(x-1)(x²-3)-5x(x+4)²-(x-5)²
c) 2x (x - 4)²(x + 5)(x - 2)(x + 2)+2(x + 5)² - (x - 1)²
d) (x + 5)² - 4 x (2 x + 3)²(2 x - 1)(x + 3)(x- 3)
e) -2 x( 3 x + 2)(3 x -2)+ 5( x + 2)²- (x -1) (2 x - 1)(2x +1)
f) (7 x - 8)(7 x + 8) - 10(2x + 3)² + 5 x (3x - 2)² - 4 (x - 5)².
g) (x²- 3)(x² + 3)- 5x²(x + 1) -(x² - 3x) (x² - 2x) + 4x(x + 2)².
Giải phương trình :
8{x+1/x}^2+4{x^2+1/x^2}^2-4{x^2+1/x^2}{x+1/x}^2=(x+4)^2
Tìm x biết:
1. (x-2)^2-(x-3)(x+3)=6
2. 4(x-3)^2-(2x-1)(2x+1)=10
3. (x-4)^2-(x-2)(x+2)=6
4.9(x+1)^2-(3x-2)(3x+2)=10
5. 3x +2(5-x)=0
6.x(2x-1)(x+5)-(2x^2+1)(x+4,5)=3,5
7, 3x^2-3x(x-2)=36
8. (3x^2-x+1)(x-1) +x^2(4-3x)=5/2
