Simplify the expression and give your answer in the form of

Simplify the expression and give your answer in the form of Your answer for the function f(x) is : Your answer for the function p(x) is :

Solution

(7x^3 - 12x^2 -4x)/( 2x^2 -10x +12)

Numerator :7x^3 - 12x^2 -4x = x( 7x^2 -12x -4) (factorise)

= x( 7x^2 -14x +2x -4) ( 7*4=28= 14*2)

= x{ 7x (x -2) +2(x-2) ----> x { (7x+2)(x-2) }

Den : 2x^2 -10x +12 = 2x^2 -6x -4x +12

=2x( x -3) - 4( x-3)

= (2x -4)(x-3) = 2 (x-2)(x-3)

f(x)/g(x) = x(7x+2)(x-2)/2(x-2)(x-3)

cancel out common terms

f(x)/g(x) = x(7x+2)(x-2)/2(x-2)(x-3) = x(7x+2)/ 2(x-3)

f(x) = x(7x +2) and g(x) = 2(x-3)