Factorizing x+3: Legal or Not?

[Michael Santos]

Homework Statement

Is it legal to factor x+3 out of x+3+h and turn it into (x+3)(1+(h/x+3))

Homework Equations

The Attempt at a Solution

 

[mfb]

Did you multiply out the result again to see if it fits?
I think you are missing brackets. 1/x+y is usually read as $\frac 1 x + y$, but what you mean is probably $\frac{1}{x+y}$ (formulas written with LaTeX).

 

[SammyS]

Homework Statement

Is it legal to factor x+3 out of x+3+h and turn it into (x+3)(1+(h/(x+3)))

Homework Equations

The Attempt at a Solution

Yes, provided you mean $\displaystyle \ (x+3)\left( 1 + \frac{h}{x+3} \right) \,.$

I inserted the missing parentheses in the above quote of your post. These are necessary when writing the fraction on a single line rather than in stacked form as pointed out by @mfb .