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There are some very useful rules when dealing with partial fractions1) For every linear factor such as ax + b in the denominator, there will be a partial fraction of the form A /...

If we want to prove it, we need to prove every odd number can be expressed as the difference of two squares, which is very easy.

Suppose this odd number to be 2n-1, then we can see 2n-1=n...

To solve these equations, our aim is to find a value of x and a value of y that satisfy both equations at the same time. By satisfy we mean, if we plug our values in for x and y then the left hand side...

The method we use to differentiate this form of equation is called the chain rule.

The chain rule is dy/dx = dy/du x du/dx

We can rememeber the right way up of the terms on ...

To solve these eliminations, we must eliminate either the x's or the y's. Either is possible but let us start with the y's. There is 2y in the first equation and (-1)y in the second, so we will have to...