## 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
[1]   Once the LHS expression has no meaning, it would not even make sense to continue.
[2]   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