Write as:
x^2/(x^2-2^2) = x/(x+2)-2/(2-x)
Using the principle that color(white)("s") a^2-b^2=(a+b)(a-b)
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color(brown)("The sort of cheating bit - not really!")
Consider -2/(2-x).color(white)(c) We need to change this such that the
color(white)()
denominator is x-2 if we whish to use the context of
color(white)()
color(white)("s") a^2-b^2=(a+b)(a-b)
Suppose we had +2/(x-2) which is the format we wish to have. If we use this is it another form of what was originally written. That is; does it have the same value?
color(green)([2/(x-2)color(red)(xx1)] ->[2/(x-2)color(red)(xx(-1)/(-1))] = -2/((2-x))
So +2/(x-2) has the same value as -2/(2-x)
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Write as:
x^2/(x^2-2^2) = x/(x+2)+2/(x-2)
This is the same as:
x^2/(x^2-2^2)=(x xx2)/((x+2)(x-2))
x^2/(x^2-2^2)=(2x)/(x^2-2^2)
As the denominators are the same we can just consider the numerators.
x^2=2x
Divide both sides by x
x=2
