Sunday, 21 September 2014

[Someone asked...] When simplifying expressions... do we factorise?

When we are asked to simplify expressions, we would usually expand to work on the like terms. However, there are occasions when we need to look out for "patterns".

Here are some possible scenarios:

1. If no variables are involved in the denominator of any algebraic fractions, we can just expand to simply.

2. If there is variable in the denominator, we'll need to see how complex it is.

In the following example, you notice that the denominator is very simple - it has only a numerical value multiplied to "x".
  • Now, we simply need to simplify the numerator like what we did (usually). 
  • When we reach Line 2, then check if there's any common factor amongst the terms in the numerator. 
  • If there is, 'take out' the common factor, just in case it can be 'cancelled' with the denominator.
  • In this case, you notice that in Line 3, we have "2x" in the numerator, which we can reduce further with the denominator "6x", resulting in what we see in Line 4.

3. In the following, you notice that the denominator seems a bit 'more complex', and there seems to be a common factor between the terms.
  • In addition, the numerator has 2 'brackets', hinting a possibility of 'reducing' with some terms in the denominator. So, do not expand the 'brackets' in the numerator yet. 
  • In Line 2, we 'take out' the common factor of the denominator.
  • Now check if there's any common factor between the numerator and the denominator., You would notice (x+2) is the common factor. 'Cancel' them and we'll get Line 3. 
  • Now, simplify and the final answer is as shown in Line 4.

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