given f(x) and g(x) i am asked to show an equality with some unknown factor (i think)

[bignaughtydog]

[h=2]given f(x) and g(x) i am asked to show an equality[/h]

f(x)= 3/sqrt(9+4x) and g(x)= 3/sqrt(1+4x)

i am asked to show that by writing

3/sqrt(9+4x)= 1/sqrt(1+(4x/9)) (and here their is some factor that i know is there, obs) but i cannot see.

)

and am then asked to substitute into one of the standard taylor series about 0 for f.give the explicity upto the term x^3 and determine the range of validity.My algebra is letting me down again.I know what i want but i dont know how to get it.

Can anyone help????

Many thanks in advance....​

 

[Freeman]

1/sqrt(1+x)=1-1/2*x+3/8*x²-5/16*x³+...
Series converges when |x|<1.

 

[bignaughtydog]

1/sqrt(1+x)=1-1/2*x+3/8*x²-5/16*x³+...
Series converges when |x|<1.

Thank you thank you thank you.