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Firstly, we are given that f(x) can be expressed in the above form, so we write this out:

(19x-2)/((5-x)(1+6x)=A/(5-x)+B/(1+6x)

We then multiply by the denominator of f(x):<...

While this question may appear unfamiliar at first, it is just a quadratic equation in disguise. Rearranging such that it equals 0:

x^2 + 5x - 36 = 0

Now this equation is re...

At first this looks quite daunting as it combines a number of different indices (powers) and a fraction. 

The rules for indices are just something that you have to learn - so don't worry ...