Question

If f(x)=2x^2-x-6 and g(x)=x^2-4 find f(x)/g(x)

Answer 1

Answer:

$\boxed{\boxed{\dfrac{f(x)}{g(x)}=\dfrac{2x+3}{x+2}}}$

Step-by-step explanation:

Here,

$f(x)=2x^2-x-6$

$=2x^2-4x+3x-6$

$=2x(x-2)+3(x-2)$

$=(2x+3)(x-2)$

And

$g(x)=x^2-4$

$=x^2-2^2$

$=(x+2)(x-2)$

Therefore,

$\dfrac{f(x)}{g(x)}=\dfrac{(2x+3)(x-2)}{(x+2)(x-2)}$

$=\dfrac{2x+3}{x+2}$