SOLUTION: Find the rational expression in simplest form that represents the sum of the recipricals of the consecutive integers x-2 and x-1. a. 2x-3 -------- (x-2)(x-1) b. x-1 ----

Algebra ->  Graphs -> SOLUTION: Find the rational expression in simplest form that represents the sum of the recipricals of the consecutive integers x-2 and x-1. a. 2x-3 -------- (x-2)(x-1) b. x-1 ----      Log On


   

Question 466252: Find the rational expression in simplest form that represents the sum of the recipricals of the consecutive integers x-2 and x-1.
a. 2x-3
--------
(x-2)(x-1)
b. x-1
--------
x-2
c. -3
----------
(x-2)(x-1)
d. -3(x-1)
----------
(x-2)
e. x-2
---------
x-1
Answer by algebrahouse.com(1659) About Me  (Show Source):
You can put this solution on YOUR website!
x - 2 + x - 1

Sum of reciprocals
= 1/(x - 2) + 1/(x - 1)
= (x - 1) / (x - 2)(x - 1) + (x - 2) / (x - 2)(x - 1) {got common denominator}

x - 1 + x - 2
-------------- {combined numerators over common denominator}
(x - 2)(x - 1)

2x - 3
-------------- {combined like terms in numerator}
(x - 2)(x - 1)

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