20x+44Find the partial-fraction decomposition of:x +2x - 35vinoitoton Iovnstni ni t to spNDn bno niomob sntd De 21A(x) d-(x)1 de anAnoitoton Iovstni ni to spnon bno niomob srltAns 7bnia

Given expression is, 20x+44x2+2x-35

Answered: 20x+44 Find the partial-fraction…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter5: Systems Of Equations And Inequalities

Section5.3: Partial Fractions

Problem 7E

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Question

20x+44
Find the partial-fraction decomposition of:
x +2x - 35vi
noitoton Iovnstni ni t to spNDn bno niomob snt
d De 21A
(x) d
-(x)1 de anA
noitoton Iovstni ni to spnon bno niomob srlt
Ans 7
bnia

Expert Solution

Step 1

Given expression is,

$\frac{20 x + 44}{x^{2} + 2 x - 35}$

Step 2

Now,

$\begin{array}{rcl} \frac{20 x + 44}{x^{2} + 2 x - 35} & = & \frac{20 x + 44}{x^{2} + 7 x - 5 x - 35} \\ = & \frac{20 x + 44}{x (x + 7) - 5 (x + 7)} \\ = & \frac{20 x + 44}{(x + 7) (x - 5)} \end{array}$

Now consider,

$\begin{array}{rcl} \frac{20 x + 44}{(x + 7) (x - 5)} & = & \frac{A}{x + 7} + \frac{B}{x - 5} \\ 20 x + 44 & = & (x - 5) A + (x + 7) B \\ 20 x + 44 & = & x (A + B) + 7 B - 5 A \end{array}$

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