[SoothingDave]

48/x(9+3)=288
48/12x=288

You beg the question in your first step. You assume that (9 + 3) is in the denominator of the expression. If you express this expression in a linear fashion (entering into a calculator or programming a computer), you need to add parentheses to make this so.

48/(x(9 + 3))

[Ironfocus]

No, nothing to do with question begging, it is simple testing of the two proposed answers.

[grateful]

You beg the question in your first step. You assume that (9 + 3) is in the denominator of the expression. If you express this expression in a linear fashion (entering into a calculator or programming a computer), you need to add parentheses to make this so.

Exactly. And a point I made earlier is that this is not an algebraic equation. Therefore, parens trumps multiplication. Once you do the equation in the parens, 2(12) becomes 2*12. There is no such thing as "implied parentheses", otherwise I could write the equation this way:

48/2*9 +3

... and argue there is an implied parentheses around the 9+3. Parentheses are always explicit. They have to be. That is their purpose.

(Btw, award winning calculus gal here, too.)