Rational Expressions (A Level only) (OCR A Level Maths: Pure)

Simplify fully 

Simplify fully 

The function  is given by .

Show that .

Hence, or otherwise, write down the real solutions to the equation

The function  is given by

Work out  and hence write down a factor of .

Work out .

Write  in the form  where  are integers to be found.

Which one of the following algebraic fractions is improper?  Explain your answer.

Find the remainder when  is divided by .

Given that 

where  are integer constants.

In terms of  and/or  as appropriate

Find the values of .

The function  is given by

where  are integer constants.

It is also given that  .

Find the values of .