Given that display style

Question

f(x)=6/(x-14),g(x)=15/(x+1)

 

find

(a) f+g

(b)f-g

(c)fg

(d)f/g

Answer 1

f(x)=6/(x-14),  g(x)=15/(x+1)

(a) f + g

f(x) + g(x) = 6/(x-14) + 15/(x+1)

Rewrite the expression with common denominator.

= [ 6(x+1) + 15(x-14) ] / [(x-14)(x+1)]

= [6x+6+15x-210] / [(x-14)(x+1)]

= (21x - 204) / [(x-14)(x+1)]

= 3(21x - 204) / [(x-14)(x+1)]

Answer 2

(b).f - g

= 6/(x-14) - 15/(x+1)

Rewrite the expression with common denominator.

= [6(x + 1) - 15(x - 14)] / [(x+1)(x-14)]

= (6x+6 -15x + 210) /[(x+1)(x-14)]

= (- 9x +216) / [(x+1)(x-14)]

= 9(-x+24) / [(x+1)(x-14)]

= 9(24-x) / [(x+1)(x-14)]

Answer 3

(c). fg

fg = [ 6/(x-14) ] [ 15/(x+1) ]

= [(6)(15)] / [(x-14)(x+1)]

= 90 / [(x-14)(x+1)]

Answer 4

(d). f/g

f/g = [6/(x-14)] / [ 15/(x+1)]

=  [6/(x-14)] [(x+1)/15]

= [6(x + 1)]/[15(x - 14)]

= [2(x + 1)]/[5(x - 14)]

= (2x+2) / (5x - 210)