Let’s suppose you are looking for some extra examples. You have probably checked all the usual websites, BBC Bitesizefor example (also available on Facebook).

Some of my students were recently looking at examples like this and wanted some further problems:

Note the thinking behind this:
You should spot that the denominator is the difference of two squares, hence (x+5)(x-5)
If we are to have any hope of simplifying when we factorise the numerator, one of the factors must be (x+5) or (x-5), of those two it must be (x-5) or we would not be able to obtain the -19x term.
Factorise the numerator: (3x-4)(x-5)

Chapter 10 on equations includes many useful algebra examples and exercises including problems of the type above (see worked example 1 on page 41 and the exercises on page 43). Note that each GCSE section has answers.
You should check any factorisation by multiplying out your answer. You could also check answers using WolframAlpha.

Note that you could enter the whole expression and simplify it – WolframAlpha will give you alternate forms; for this type of question you are require to give the simplest single fraction that you can.