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The rational function is the proper fraction, when degree of the polynomial in numerator is less than degree of the polynomial in denominator. Examples: x+2 / x^2-x+1, x^2-3x+1 / x^5-3x, x / x^8+1, x^7+x^3-3x^2+5x+1 / x^9+x^8+x^7-4x^2+3x+1. The rational function is the improper fraction, when degree of the polynomial in numerator is greater than or equal degree of the polynomial in denominator. Examples: x^3+5x / x+1, x^7+8 / x^7+3x, 3x^5-2x^4+3x-3 / 2x^2+4x+1, 3x^8+1 / 2x^3+x^2-3x+1. Every improper fraction can be written in form sum of the polynomial and the proper fraction.