Question

let f(x)=2/x-1 and g(x)=2x-2/3x+3.find.
a)f+g
b)fg
c)domain of(f+g)and fg

Answer 1

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Answer 2

Assuming you mean
f(x)=2/(x-1) and g(x)=(2x-2)/(3x+3)
then g(x) = 2(x-1)/(3(x+1))

f+g = 2/(x-1) + (2/3)(x-1)/(x+1)
= ( 6(x+1) + 2(x-1)(x-1))/(3(x^2 - 1))
= (6x + 6 + 2x^2 - 4x + 2)/(3(x^2 - 1)
= (2/3)(x^2 + x + 4)/(x^2 - 1)

you do fg, which means you just multiply them

domain of f+g is x∈R, x ≠ ±1

Answer 3

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Answer 4

Domain of(f+g)and fg