Simplifying Rational Expressions

This item is taken from IGCSE Mathematics (0580) Paper 43 of October/November 2010.


To deal with this item, let us summarize the details of the problem:
   (a) Syllabus area: Algebra
   (b) Specific topic: Simplifying Rational Expressions

We will try to answer this item in different methods. 
For the first method, we need to find the LCD (least common denominator) of the fractional expressions. Here are the steps needed:

Another method is the following:

Therefore,

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