Maths
posted by Nawaf .
Write the following expression into its simplest form?
(1/x11/xsquare11/x+14/xsquare+1)/
xraise to 4/xsquare1
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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