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f(x)=(x^2-9x+15)/(x^2-5)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

x2−9x+15x2−5\frac{x^2-9x+15}{x^2-5}

Step-by-step Solution

1

Divide x2−9x+15x^2-9x+15 by x2−5x^2-5

;x2−5;;1;;;x2−5);x2−9x;+15;;‾;x2−5;−x2−;xn+5;;‾−x2+5;;;−9x;+20;;\begin{array}{l}\phantom{\phantom{;}x^{2}-5;}{\phantom{;}1\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-5\overline{\smash{)}\phantom{;}x^{2}-9x\phantom{;}+15\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-5;}\underline{-x^{2}\phantom{-;x^n}+5\phantom{;}\phantom{;}}\\\phantom{-x^{2}+5\phantom{;}\phantom{;};}-9x\phantom{;}+20\phantom{;}\phantom{;}\\\end{array}
2

Resulting polynomial

1+−9x+20x2−51+\frac{-9x+20}{x^2-5}

Final answer to the exercise

1+−9x+20x2−51+\frac{-9x+20}{x^2-5}

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Main Topic: Polynomial long division

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division.

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