For Exercises 55-56, find the partial fraction decomposition for the given expression. [Hint: Use the substitution
and recall that
.]
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College Algebra (Collegiate Math)
- Can you explain why a partial fraction decomposition is unique? (Hint: Think about it as a system of equations.)arrow_forwardMatch the rational expression on the left with the correct partial fraction decomposition form on the right. x2-2x+3x2x-4x2+5 a. Ax+Bx2+Cx3+Dx4+Ex-4+Fx+Gx2+5 b. Ax+Bx-4+Cx-42+Dx-43+Fx+Gx2+5+Hx+Ix2+52 c. Ax+Bx2+Cx-4+Dx2+Ex+Fx3+5 d. Ax+Bx2+Cx3+Dx-4+Ex-42+Fx+Gx2+5 e. Ax+Bx-4+Cx+Dx2+5 f. Ax+Bx2+Cx-4+Dx+Ex2+5arrow_forward(a) How do we express a rational function r as a partial faction decomposition? (a) Given the form of the partial fraction decomposition. (i) 2x(x5)(x1)2 (ii) 2x(x5)(x21) (iii) 3x+1x(x2+1)2arrow_forward
- Write out the form of the partial fraction decomposition ofthe function (as in Example 6). Do not determine the numericalvalues of the coefficients. x6 /(x 2 -4 )arrow_forwardIs the following statement correct? Justify your answer and complete solving the problem. For the rational expression x/(x+1)(x-2)^2, the partial fraction decomposition is of the form A/x+1 + Bx+C/(x-2)^2arrow_forwardThe partial fraction decomposition of 4 / (x−3)(x−7) can be written in the form of A/ x−3 + B/x−7, whereA= ,B= .arrow_forward
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