<p>When finding the partial fraction decomposition of a rational expression how do you know how many fractions to break the denominator into?</p>
<p>Example:</p>
<h2>X^2+12x+12</h2>
<p>(X^3-4x)</p>
<p>My teacher told us that we were to break the denominator down to all possible combinations that would make the final denominator, but if I were to do that to this problem I'd get seven different fractions, is this correct or should I stick with the three basic fractions?</p>
<p>hello............</p>
<p>All depends. Damn I need LaTeX...</p>
<p>x^3 - 4x factors to x(x+2)(x-2) then you will need three if you want to do it completely formal. Then youll set the variables equal to the numerator and then do some work.</p>
<p>yeah, I was trying to break it into all possible quanities that might have given the denominator, but that is actually an infinite number of possibilites, way to over analyze.</p>
<p>Use the "cover-up" method.</p>
<p>factorize the denominator(x(x-2)(x+2)). In the problem the separate denominators would be a/x, b/(x-2), c/(x+2). Find the values of a,b,c and the problem is solved.</p>