A lot of people are having trouble with this math problem that requires some basic algebra

[athena]

87. In that case, you know what is meant from the context.

You know from context and experience, and simple logic, that the writer does not mean 1 - x^2 - k^2 x^2, since he would then have written that, or 1 - (1 + k^2) x^2. It is not technically correct, just as it is not technically correct to omit c in physics expressions, but the experienced reader will know what is meant from the context. That doesn't mean the rules have been thrown out the window.

Furthermore, it is not a "parsing convention" to write 1 - x^2 x 1 - k^2 x^2 to mean (1 - x^2) . (1 - k^2 x^2). If it were a parsing convention, the writer would not have used - (1 + m x^2) (1 + n x^2) and other similar expressions on the previous page.

Now, when you see an expression like
9 – 3 ÷ 1/3 + 1,
there is no context, so you go back to using the rules you were taught in elementary school. The fact that two different symbols for division have been used should not cause any distraction, since you instinctively interpret 1/3 as a number and divide 3 by that, which gives you 9, so that the final result is 1.

Since my gender apparently makes it difficult for some people to agree with an obvious point I made, let me say that I showed the expression to my husband, who is also a physicist, and he also came up with 1 on the spot.