SOLUTION: divide: x^2-1/x^2+3x+2 ÷ x^2+2x-3/x^2+x-2 a. x-1/x+3 b. x+1/x+3 c. x+3/x-1 d. x-1/x+1

Algebra ->  Rational-functions -> SOLUTION: divide: x^2-1/x^2+3x+2 ÷ x^2+2x-3/x^2+x-2 a. x-1/x+3 b. x+1/x+3 c. x+3/x-1 d. x-1/x+1      Log On


   

Question 89246: divide: x^2-1/x^2+3x+2 ÷ x^2+2x-3/x^2+x-2
a. x-1/x+3
b. x+1/x+3
c. x+3/x-1
d. x-1/x+1
Answer by malakumar_kos@yahoo.com(315) About Me  (Show Source):
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divide: x^2-1/x^2+3x+2 ÷ x^2+2x-3/x^2+x-2
a. x-1/x+3
b. x+1/x+3
c. x+3/x-1
d. x-1/x+1

Factorise x^2-1 = (x+1).(x-1)
x^2+3x+2 = x^2+2x+1x+2 = x(x+2)+1(x+2) = (x+2).(x+1)
x^2+2x-3 = x^2+3x-x-3 = x(x+3)-1(x+3) = (x+3).(x-1)
x^2+x-2 = x^2+2x-x-2 = x(x+2)-1(x+2) = (x+2).(x-1)
x^2-1/x^2+3x+2 divided by x^2+2x-3/x^2+x-2
= (x+1).(x-1)/(x+2).(x+1) divided by (x+3).(x-1)/(x+2).(x-1)
= (x-1)/(x+2) divided by (x+3)/(x+2)
= (x-1).(x+2)/(x+2).(x+3) = (x-1)/(x+3)