[x^(-1) - x^(-3)] / (x^3 - x^2)

Question

Eliminate negative exponents and simplify; can't figure out what to do when there is addition and subtraction involved with exponents. Here is the problem again:

 

(X^{-1 }– X^-3) / (X³ – X²) 

 

And here's another similar problem if you're up for it:

 

(2x^-1 + 3y^-1) / (9x² - 4y²)

Answer 1

(x+1)/x5 is the correct answer; see my comment which corrects an error in Eric C's factoring.

Answer 2

Hey Addy.

 

An easier way to look at negative exponents is as reciprocals of a positive exponent.

 

x^-3 = 1/x³

 

Using this fact, we can rewrite your expression as:

 

(1/x - 1/x³) / (x³ - x²)

 

Find a common denominator for the numerator.

 

(x²/x³ - 1/x³) / (x³ - x²)

 

((x² - 1)/x³) / (x³ - x²)

 

Now simplify. The x³ in the numerator will combine with the denominator.

 

(x² - 1) / (x³(x³ - x²))

 

Factor out an x² from the expression in the denominator. It'll multiply with x³ to become x⁵.

 

(x² - 1) / (x⁵(x² - 1))

 

Cancel out the x² - 1 terms.

 

1/x⁵

 

Hope this helps.