<p>I got into a pretty bad head-on collision today, but luckily no one was injured (except the poor cars :( ) </p>
<p>I have some calc homework that I cannot figure out. Possibly help me so I can just go to bed and end this awful day?</p>
<p>Could you explain how to make partial fractions with this:</p>
<p>(x^2+8)/(x^2-5x+6)</p>
<p>We've been doing that whole thing where you do something like this:</p>
<p>x+8/x^2-4 = (A/(x-2)) + (B/(x+2))</p>
<p>Help with the given problem??</p>
<p>First, you must factor the denominator into (x-3)(x-2).</p>
<p>Then, you can say (x^2+8)/[(x-3)(x-2)] = A/(x-3) + B/(x-2).</p>
<p>Cross multiply to get x^2+8=A(x-2) + B(x-3).</p>
<p>Now, you substitute convenient values of x to find the constants. To find A, let x=3 so that B is multiplied by 0 and thus cancels out. Then, you can solve for A. Likewise, to find B, let x=2 so that A is multiplied by 0 and canceled. Finally, you substitute A and B back in to A/(x-3) + B/(x-2).</p>
<p>I hope that was clear, especially after a car accident. I may have done it wrong though since you may have to do long division or something like that. Take care.</p>
<p>Yeah I understand that, and that’s what I did, however apparently it is wrong according to the back of my text book. It says that it should be 1 - …all the A and B stuff.</p>
<p>Yeah, you do have to do long division first. Do you remember how? You should get 1+(5x-2)/(x^2-5x+6), then apply partial fractions to the part after the 1.</p>
<p>Edit–I mean 5x+2.</p>
<p>Oh okay thanks so much!</p>