A rational function g(x) is such that g(x) = f(x) wherever f(x) is defined. Find the value of a and b.

Question

f(x) = (2x-2)/ x²+x-2

g(x) = a/ b+x

 

Answer 1

f(x) = (2x-2)/(x²+x-2)

 

       = 2(x-1)/[(x+2)(x-1)]

 

       = 2/(x+2) where x ≠ 1,-2

 

g(x) = a/(b+x)

 

f(x) = g(x) when a=b=2