Rational Functions 
f(x) = (x^2 + 2x - 7)/(x - 2)

You can simplify with long division of polynomials

You can also simplify with cancellation

4(a-3)/4 = (4/4)(a-3) = a-3

Addition and subtraction

Same as normal fractions - find a common denominator and add or subtract the numerator

Multiplication

Factor out both sides and use cancellation to simplify the equation. If you cancel a factor in the denominator that limits the domain of one of the functions, you need to explicitly provide that limitation in your simplified form because it limits the domain of the product.

(4x^2 - 1)/(x^2 - 4) * (x-2)/(2x-1)

(2x+1)(2x-1)/(x+2)(x-2) * x-2/2x-1 // cancel out 2x-1 and x-2

2x + 1 / x + 2 with x != 1/2 or 2

Division

  1. Factor out both sides
  2. List all restrictions. Keep in mind all areas of the equation that can not be 0 (anything)/(x!=0) / (x!=0)/(x!=0)
  3. Multiply against the reciprocal of the devisor
  4. Cancel common factors
  5. List the solution with it's restrictions
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