Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients. a) x4+6x5+7x3 b) 2(x2−9)2

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Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.  a) x4+6x5+7x3  b) 2(x2−9)2

Sadie Eaton · Accepted Answer

Step 1 a) We have to factor the denominator. x4+6x5+7x3 =x4+6x3(x2+7) Then for x3 we will get three fractions with denominators x, x2 and x3. And Another fraction will have denominator x2+7. So the partial fraction will look like: =Ax+Bx2+Cx3+Dx+Ex2+7 Where A,B,C,D and E are constants. Answer: =Ax+Bx2+Cx3+Dx+Ex2+7 Step 2 b) We have to factor the denominator. 2(x2−9)2 =2((x+3)(x−3))2 =2(x+3)2⋅(x−3)2 Then for (x+3)2 we will get two fractions. One with denominator (x+3) other with denominator (x+3)2. For (x−3)2 we will get two fractions. One with denominator (x−3) other with denominator (x−3)2. So the partial fraction will look like: =Ax+3+B(x+3)2+Cx−3+D(x−3)2 Where A,B,C and D are constants. Answer: =Ax+3+B(x+3)2+Cx−3+D(x−3)2

Write out the form of the partial fraction decomposition of the function. Do not

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