# Maths

Write the following expression into its simplest form?

(1/x-1-1/xsquare-1-1/x+1-4/xsquare+1)/
xraise to 4/xsquare-1

Let's use the symbol ^ to mean "raised to the power of" when using exponents.

I'll try to decipher your expression:
[1/(x - 1) - 1/(x^2 - 1) - 1/(x + 1) - 4/(x^2 + 1)] / [x^4/(x^2 - 1)]

Try to factor whenever you can:
[1/(x - 1) - 1/(x + 1)(x - 1) - 1/(x + 1) - 4/(x^2 + 1)] / [x^4/(x + 1)(x - 1)]

Let's find a common denominator, which is (x^2 + 1)(x + 1)(x - 1).

Using the common denominator in the numerator:
[1(x^2 + 1)(x + 1)/(x^2 + 1)(x + 1)(x - 1) - 1(x^2 + 1)/(x^2 + 1)(x + 1)(x - 1) - 1(x^2 + 1)(x - 1)/(x^2 + 1)(x + 1)(x - 1) - 4(x + 1)(x - 1)/(x^2 + 1)(x + 1)(x - 1)] / [x^4/(x + 1)(x - 1)]

Simplifying:
[(x^2 + 1)(x + 1) - (x^2 + 1) - (x^2 + 1)(x - 1) - 4(x + 1)(x - 1)]/(x^2 + 1)(x + 1)(x - 1) * (x + 1)(x - 1)/x^4 --> Invert the fraction and multiply (I'm using * to mean multiply).

[(x^2 + 1)(x + 1) - (x^2 + 1) - (x^2 + 1)(x - 1) - 4(x + 1)(x - 1)]/ x^4(x^2 + 1)

[(x^3 + x + x^2 + 2 - x^2 - 1 - x^3 - x + x^2 + 1 - 4x^2 + 4)]/[(x^6 + x^4)]

Combining like terms:
(-3x^2 + 6)/(x^6 + x^4)

And that's as far as we can go on this one if I haven't missed anything. I hope this is what you were asking.

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