## Wednesday, February 17, 2016

Problem

Introduction
Assuming no typing errors, this is a tricky Secondary 2 question involving an equation with algebraic fractions.  How to solve it?  How to present the solution?

Solution

Remarks
   Once the LHS expression has no meaning, it would not even make sense to continue.
   This is a proof by contradiction type of argument.
It turns out that not all algebraic equations are soluble (or solvable).  This problem is one case in point.  The “unknown”  m  cannot be 5/2 because that would make the expression undefined.  But if you substitute any other value, you always end up with nonsense like “15 = 0”.  So no matter what, there is no solution.  In other words, there is no value of  m  that you can substitute into the equation that makes it a true statement.

H05. Work backwards
H08. Make suppositions

Suitable Levels
Lower Secondary Mathematics (Sec 2 ~ grade 8)
GCE ‘O’ Level “Elementary” Mathematics
* other syllabuses that involve algebra
* any learner who is interested in algebra