12. [0/1 Points] DETAILS PREVIOUS ANSWERS OSPRECALC1 9.4.218. Find the partial fraction decomposition of the expression with a denominator containing nonrepeating linear factors. \frac{7x}{x^2 - 16} Recall what it means to decompose a single fraction to its equivalent partial fractions. What are the distinct linear factors of the denominator? Set the each numerator is a distinct symbolic constant, A or B. Multiply both sides of the equation by the least common denominator. How is the resulting equ Additional Materials eBook Partial Fraction Decomposition Example Video
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First, factorize the denominator into its distinct linear factors. For example, if the denominator is (x+1)(x-2)(x+3), the distinct linear factors are (x+1), (x-2), and (x+3). Show more…
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Question 12 (7 points) For the following partial fraction decomposition problem, you are given the setup below: (2x^2+4)/(x^3+5x^2+4x) = A/x + B/(x+1) + C/(x+4) Solve for the values of A, B, and C. A= B= C= Question 13 (6 points) The following equation is a result of performing the process used to decompose partial fractions. 18x^2 + 19x - 5 = (Ax + B)(2x + 3) + C(x^2 + x + 1) After using all of the convenient x-values it is determined that C = 4. Determine the values of A and B. A= B=
Claire R.
$3-12$ . Form of the Partial Fraction Decomposition Write the form of the partial fraction decomposition of the function (as in Example 4). Do not determine the numerical values of the coefficients. $$\frac{1}{(x-1)(x+2)}$$
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Determine the partial fraction decomposition for each of the given rational expressions. Hint: In Exercises $17,18,$ and $26,$ use the rational roots theorem to factor the denominator. $$\frac{2 x}{32 x^{2}-12 x+1}$$
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