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This denominator is irrational because it contains a surd. To rationalise the denominator we multiply the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of the ...

To start with, we need to notice the difference between each of the terms in the sequence. As this is a linear sequence, the sequence increases or decreases by the same amount between each term. In this q...

The first step is to expand out the brackets, we can do this more simply by splitting the equation into two parts. In order to expand the first half of the equation, 3(m+4), you must times both m and 4 by...

This question wants you to "complete the square". To start this question we put a = (coefficient of x)/2 = 6/2 = 3.So far we have 𝑥²+6𝑥+11 = (𝑥+3)²+b. We now need to find b. We can expand and si...

First, we substitute in our functions f and g. We can do this in two ways.1) Find g^-1:As g takes 3 from x, the inverse operation must add 3 to x. So g^-1(x) = x + 3Then our equation gf(x) = g^-1(x) becom...