Factorizing x+3: Legal or Not?

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SUMMARY

Factoring x+3 out of the expression x+3+h is legal and can be expressed as (x+3)(1+(h/(x+3))). The discussion emphasizes the importance of using proper parentheses to avoid ambiguity in mathematical expressions. Specifically, the correct interpretation of fractions in LaTeX notation is crucial for clarity. The community confirms that the factorization is valid when the parentheses are correctly placed.

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Michael Santos
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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

 
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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).
 
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Michael Santos said:

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 .
 
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