Question

Si f(x)=x^2-1, g(x)=2x+3 y h(x) 2/(x+1) halla:

a. f(x)+g(x)
b. f(x)+h(x)
c. h(x)-g(x)
d. g(x)-h(x)
e. f(x).g(x)
f. g(x).h(x)
g. f(x)/g(x)
h. f(x)/h(x)

Por favor ayudenme

Answer 1

a. f(x)+g(x) = x^2-1 + 2x + 3
b. f(x)+h(x) = x^2-1 + 2/(x+1) = {(x^2-1 )(x+1) + 2}/(x+1)
= (x^3+x^2-x-1+2)/(x+1)
= (x^3+x^2-x+1)/(x+1)
c. h(x)-g(x) = 2/(x+1) - (2x+3)
= {2-(2x+3)(x+1)}/(x+1)
= {2-(2x^2+2x+3x+3)}/(x+1)
= (2-2x^2-2x-3x-3)/(x+1)
= (-2x^2+2x+3x-1)/(x+1)
d. g(x)-h(x) = 2x+3 - 2/(x+1)
= {(2x+3)(x+1)-2}/(x+1)
= (2x^2+2x+3x+3-2)/(x+1)
= 2x^2+2x+3x+1)/(x+1)
e. f(x).g(x) = (x^2-1)(2x+3)
= 2x^3+3x^2-2x-3
f. g(x).h(x) = (2x+3){2/(x+1)}
= (4x+6)/(x+1)
g. f(x)/g(x) = (x^2-1)(2x+3)
= (2x^3+3x^2-2x-3)
h. f(x)/h(x) = (x^2-1)(2/(x+1))
= (2x^2-2)/(x+1)