Posted by **Nawaf** on Tuesday, November 21, 2006 at 8:42am.

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.

## Answer this Question

## Related Questions

- CALCULUS - Y=(XSQUARE + 1 OVER XSQUARE - 1) CLOSE PARENTHESIS TO THE 3 POWER...
- ssc maths - 2 xsquare y -3 xsquare+ 4 y=2010
- math - 2xsquare -8x -42 over 6xsquare divided by xsquare -9 over xsquare -3x in ...
- srinvas - solve ;2 xsquare y-3 xsquare+4 y=2010
- pure maths - Factorize Xsquare-6x-3
- Further maths - Two functions f and g are defined over the set of R of real ...
- 9th grade - whats the answer for xsquare+12x+20=0
- math - Find all numbers that are not in the domain of the function. Then give ...
- math - solve the following system of equations algebraically or graphically for ...
- math, algebra,correction & help - directions are: write each fraction in ...