Given f(x)=4x2+19x−5 and g(x)=4x2−x .
What is (fg)(x)?
I think you mean ( f / g) x =
f (x) / g(x) =
[ 4x^2 + 19x - 5 ] / [ 4x^2 - x ] factor numerator / denominator
Note..it you're having trouble factoring....try factoring the "easier" thing, first....this is the denominator
[ 4x^2 + 19x - 5 ] / [ x (4x - 1 ) ] guess that the numerator includes 4x - 1 as a factor
[ ( 4x - 1) ( x + 5 ) ] [ x (4x - 1 ) ]
Note that the numerator factors perfectly..."cancel" the 4x - 1 on top/bottom
(x + 5 ) / x x not equal to 0, 1/4