As an aspiring amateur engineer, I like to do a lot of self studies in mathematics.
Right now, I am about to wrap up my studies of algebra through Addison/Wesley's "Intermediate Algebra", college textbook.
I'm checking my answers for section 7.3.'Complex Fractions', and I am confused about whether I am delivering what would be technically the proper answer, consider the following solutions to the evaluation of complex fractions(Sorry, I don't know how to use MathJax):
$$\frac{x^2+5x+4}{x^2+5x+10}$$
and also...
$$\frac{m^2+6m-4}{m(m-1)}$$
In the first problem, the trinomial in the numerator has the factors of $(x+1)$ and $(x+4)$, yet the product of the factors is given. The same is done in the denominator of the first problem.
In the second problem, they simply have expressed the denominator as the factors of a number $m$ and $(m-1)$. Why not, like in the first solution, express it as the product of those factors?
Is the book just vaguely telling me that there are multiple ways to express these solutions? Or is there some widely accepted convention among mathematicians that I'm not getting?