Operaciones racionales con polinomios

1.) 3/(x-1) + x/(x+2)

 

((3x+6)+(x^2-x))/ (x^2 -x +2x-2)

 

(x^2 +2x+6)/ (x-1)(x+2)

 

 

3.) ((x/y)+1)/ (1-(x/y))

 

(x+y)/y / (y-x)/y

 

-(x+y)/ (x-y)

 

 

 

5.) (x^(5/2) - x^(1/2)) / (x^2 -1)

 

x^(1/2)

 

  

7.) (x(2+x)^(-2/3) +(2+x)^(1/3))/ (2+x)^(-2/3)

 

x +((2+x)^(1/3))/ (2+x)^(-2/3)

 

1/3 - (-2/3)= 3/3

 

x+(2+x)=2+2x=

 

2(1+x)

 

  

9.) (-x+3)(-x+5)

 

x^2 -5x -3x +15

 

x^2 -8x+15

  

 

11.) (x^2 -25)/ (3x^2+11x +10) * (4x+8)/ (x^2 -2x -15)

 

((x+5)(x-5))/ (3x+5)/(x+2) *   (4x+8)/(x-5)(x+3)

 

((x-5))/ (3x+5)/(x+2) *   (4x+8)/(x+3)

 

((x-5))/ (3x+5)/(x+2) *   4(x+2)/(x+3)

 

((x-5))/ (3x+5)/ *   4/(x+3)

 

4(x+5)/ (3x+5)(x+3)

 

 

13.) 2/xy - (3y^2 -x^2)/xy^3 + (xy+y^2)/ (x^2 y^2)

 

(x^3 +y^3)/ (x^2 y^2)

 

 

15.) 1/ (2x-3y) - (x+y)/(4x^2 -9y^2)

 

(x+2y)/ ((2x+3y)(2x-3y))

 

 

17.) (2x^(1/3) (x-2)^(2/3) - 5x^(4/3) (x-2)^-(1/3))/ (-3x-4)x^1/3

 

(x-2)^(-1/3)

  

 

19.) ((x-a)(4x+8)(x+b))/ (x^2 +x(a+b)+ ab)

 

(x^2 +bx+ax+ab)(4x+8) /(x^2 +x(a+b)+ ab) (4x+8)