Question

Find f(x) divided by g(x)

f(x)=2x^2+x-6 and g(x)=x^2-4

A) 2x-3/x+2
B) 2x+3/x-2
C) 2x+3/x+2
D) 2x-3/x-2

Answer 1

(2x - 3)/(x-2)

Explanation:

divide the given equations :

(2x^2 +x -6) / (x^2 -4)

but first do some rearrangements

x^2 - 4 = (x - 2) × (x + 2)

and

(2x^2 + x - 6) = (2x -3) × (x + 2)

when you write the whole equation as a fraction

(x+2) will be eliminated from both sides and only (2x - 3)/(x - 2) will be left

we can't do further calculations so it's the simplest way to write it