Question

Given the rational expression 12x²-108/36x-108, which of the following represents its simplest formA) 12(x+3)/36B) x²-9/3(x-3)C) x+3/3D) x/3

Answer 1

Given the expression :

`(12x^2-108)/(36x-108)=(12(x^2-9))/(36(x-3))=(12(x+3)(x-3))/(12\cdot3\cdot(x-3))=(x+3)/(3)`

Note : we have taken 12 as common from 12x²-108, the result will be 12 (x²- 9 )

and 36 as a common from 36x-108, the result will be 36 ( x - 3 )

(x²- 9 ) = ( x - 3) ( x + 3) [ the difference between two complete squares ]

then we have simplified the rational expression

so, the answer is option c) (x+3)/3