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Simplifying numerator

I'm writing a script to create quotient rule exercises, but I cannot coerce the fraction to simplify as desired. In particular, I'd like latex(sol) to look like the following:

 \frac{2x^2+4}{(x^2+1)^2} 

But evaluating

 (2*x+4)/(x^2+1)^2 

always seems to factor the numerator to get

 2*(x + 2)/(x^2 + 1)^2 

and simplify_full() seems to only expand the denominator, not the numerator:

 2*(x + 2)/(x^4 + 2*x^2 + 1) 

Simplifying numerator

I'm writing a script to create quotient rule exercises, but I cannot coerce the fraction to simplify as desired. In particular, I'd like latex(sol) to look like the following:

 \frac{2x^2+4}{(x^2+1)^2} \frac{2x+4}{(x^2+1)^2} 

But evaluating

 (2*x+4)/(x^2+1)^2 

always seems to factor the numerator to get

 2*(x + 2)/(x^2 + 1)^2 

and simplify_full() seems to only expand the denominator, not the numerator:

 2*(x + 2)/(x^4 + 2*x^2 + 1) 

Simplifying numerator

I'm writing a script to create quotient rule exercises, but I cannot coerce the fraction to simplify as desired. In particular, I'd like latex(sol) to look like the following:

 \frac{2x+4}{(x^2+1)^2} 

But evaluating

 (2*x+4)/(x^2+1)^2 

always seems to factor the numerator to get

 2*(x + 2)/(x^2 + 1)^2 

and simplify_full() seems to only expand the denominator, not the numerator:

 2*(x + 2)/(x^4 + 2*x^2 + 1) 

For clarity, I think the general problem is this (perhaps?) surprising phenomenon: latex(f/g) doesn't seem to respect whether the expression f is factored or not.