let f,g and h be three functions defined as.....

Question

f(x)= 6x^2-19x+3

g(x)= 7x-6/6x-1

h(x)=7x^2+15x-18

find and if possible simplify and show all work
(h/fg)(x)

Answer 1

Given functions f(x) = 6x^2-19x+3

= 6x^2-18x-x+3

= 6x(x-3)-1(x-3)

= (6x-1)(x-3)

g(x) = (7x-6)/(6x-1)

f(x)g(x) = (6x-1)(x-3)*(7x-6)/(6x-1)

fg(x) = (7x-6)(x-3)

h(x) = 7x^2+15x-18

= 7x^2+21x-6x-18

= 7x(x+3)-6(x+3)

= (x+3)(7x-6)

(h/fg)x = (x+3)(7x-6)/(7x-6)(x-3)

= (x+3)/(x-3)