Importance of using parentheses on alt.algebra.help

Although incorrect, it is not uncommon on alt.algebra.help for someone to transcribe something similar in form to $\frac{x+1}{x-1}$ as:

x+1/x-1.

Since this is a fairly common issue, many will ask, ``Do you mean x+(1/x)-1 or do you mean (x+1)/(x-1)? In other words, it will not necessarily be assumed by everyone that what is written is what actually is intended.

Let $x=2$ . Does the above properly evaluate to 3 as intended? Division (denoted by /) has precedence over addition and subtraction, therefore this expression is properly evaluated by performing the division $1 \div 2$ , adding the result to 2, then subtracting 1 from that result, resulting in $\frac{3}{2}$ . In many cases, this is not what is intended when the statement is ``written'' on alt.algebra.help. Even if it was the intention, many here will ask for clarification if not otherwise clear from the context.

If $\frac{x+1}{x-1}$ is intended, it is necessary to use parentheses when transcribing this and similar expressions on alt.algebra.help. The original fraction can be clearly, and properly, transcribed as:

(x+1)/(x-1).

Not only does this properly evaluate as intended, it also erases any reasonable doubt one may otherwise have of your intention.

What if your intention really is x+1/x-1? Although not technically necessary, it is highly recommended that you use parentheses, as in:

x+(1/x)-1.

The liberal use of parentheses here not only adds clarity but also indicates this really is your intention, and should prevent others from asking for clarification.

Similar issues arise while transcribing expressions involving exponents. For example, it would be incorrect to transcribe what appears as $x^{y+1}$ by writing:

x^y+1.

This is really saying, ``Raise x to the power of y, then add 1,'' which is considerably different from what $x^{y+1}$ is saying. What we really want to say is, ``Raise x to the y+1 power.'' This can be properly transcribed as:

x^(y+1).

What if your intention really is x^y+1? Depending on the context it may add clarity if you use parentheses anyway, as in:

(x^y)+1.

The liberal use of parentheses here not only adds clarity but also indicates this really is your intention, and should prevent others from asking for clarification. Note that in some contexts the intent is clear even without parentheses, as in:

ax^2+bx+c=0.

Here, it is clear from the context (standard quadratic form) that we definitely do not intend:

ax^(2+bx+c)=0

...but rather ax^(2) + bx + c = 0.

Note that it is possible to overdo it. For example, it doesn't add any clarity to write:

x^([(y)+1])

...as opposed to x^(y+1). Rather, the superfluous parentheses and brackets can arguably distract the reader.

In short, use parentheses and brackets if needed to make your intent clear. Otherwise, readers of your question may make certain assumptions that may be inaccurate, or may need to ask for clarification. Either may delay a useful answer to your question.