Question

Działania arytmetyczne na wyrażeniach wymiernych.

Wykonaj działania.

a) (x-1)/(1-x) + (3x+5)/(x-1) +1

b) (x+1)/(x+5) - (x+3)/(x+2) +x

c) (x+2)/x2-9) - (x+4)/(x+3)

d) (3x-1)/(x+2) + (x2-2)/(x2-4)

Answer 1

a) (x-1)/(1-x) + (3x+5)/(x-1) +1 = (x-1- 3x-5 + 1-x)/(1-x) = (3x-3) /(1-x)= -3(1-x)/(1-x) =-3

b) (x+1)/(x+5) - (x+3)/(x+2) +x = [(x+1)(x+2) -(x+3)(x+5) +x (x+5)(x+2)]/(x+2)(x+5)=

= [x^2+ 3x +2 -x^2 - 8x -15 +x(x^2 + 7x +10)/ (x+2)(x+5)=                                        [-5x -13 +x^3+7x^2 +10x]/(x+2)(x+5)=[x^3+7x^2 + 5x- 13]/(x+2)(x+5)=

=[x^3+7x^2 + 5x- 13]/x^2 + 7x +10

c) (x+2)/x2-9) - (x+4)/(x+3) = [x+2 - (x+4)(x-3)]/(x^2 -9)=

=[x+2 -x^2+3x-4x+12]/ (x^2 -9)=(-x^2 +12)/(x^2-9)

d) (3x-1)/(x+2) + (x2-2)/(x2-4) =[(3x-1)(x-2)+x^2 -2]/(x^2 -4)=

= [3x^2 - 7x +2+x^2 -2] /(x^2 -4)= (x^2 - 7x)/(x^2 -4)