Yahoo Answers: Answers and Comments for Express (2x5)/[(x2)(3x1)(2x+5)]? [Mathematics]
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From Anonymous
enUS
Tue, 25 Jun 2019 18:23:01 +0000
3
Yahoo Answers: Answers and Comments for Express (2x5)/[(x2)(3x1)(2x+5)]? [Mathematics]
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From az_lender: (2x  5)/[(x2) (3x1) (2x+5)]
= A/(x2) + B/(...
https://answers.yahoo.com/question/index?qid=20190625182301AA44o9v
https://answers.yahoo.com/question/index?qid=20190625182301AA44o9v
Tue, 25 Jun 2019 19:25:55 +0000
(2x  5)/[(x2) (3x1) (2x+5)]
= A/(x2) + B/(3x1) + C/(2x+5) =>
2x  5 = A(6x^2 + 13x  5) + B(2x^2 + x  10) + C(3x^2  7x + 2) =>
5 = 5A  10B + 2C;
2 = 13A + B  7C;
0 = 6A + 2B + 3C.
Now you solve the three equations simultaneously the same way you would have done it in high school. I would start by eliminating "B" from the last two equations, obtaining 4 = 20A  17C. Then by eliminating "B" from the first two equations, obtaining 15 = 125A  68C. Then eliminate "C" from this pair, obtaining 1 = 45A. I can see my A = 1/45 in the given answer, but I can't guess where the 39 came from, hmm. Anyway, check my work and keep going from there.

From King Leo: .
( 2x  5 ) / [ ( x  2 )( 3x  1 )( 2x + 5 )...
https://answers.yahoo.com/question/index?qid=20190625182301AA44o9v
https://answers.yahoo.com/question/index?qid=20190625182301AA44o9v
Tue, 25 Jun 2019 19:34:31 +0000
.
( 2x  5 ) / [ ( x  2 )( 3x  1 )( 2x + 5 ) ]
( 2x  5 ) = A( 3x  1 )( 2x + 5 ) + B( x  2 )( 2x + 5 ) + C( x  2 )( 3x  1 )
( 2x  5 ) = A( 6x² + 13x  5 ) + B( 2x² + x  10 ) + C( 3x²  7x + 2 )
( 6A + 2B + 3C )x² = 0
( 13A + B  7C )x = 2x
5A  10B + 2C = 5
A = 1/45, B = 39/85, C = 40/153

From Captain Matticus, LandPiratesInc: a/(x  2) + b/(3x  1) + c/(2x + 5) = (2x  5)...
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https://answers.yahoo.com/question/index?qid=20190625182301AA44o9v
Tue, 25 Jun 2019 19:19:42 +0000
a/(x  2) + b/(3x  1) + c/(2x + 5) = (2x  5) / ((x  2) * (3x  1) * (2x + 5))
Multiply through by (x  2) * (3x  1) * (2x + 5)
a * (3x  1) * (2x + 5) + b * (x  2) * (2x + 5) + c * (x  2) * (3x  1) = 0x^2 + 2x  5
a * (6x^2  2x + 15x  5) + b * (2x^2  4x + 5x  10) + c * (3x^2  x  6x + 2) = 0x^2 + 2x  5
a * (6x^2 + 13x  5) + b * (2x^2 + x  10) + c * (3x^2  7x + 2) = 0x^2 + 2x  5
(6a + 2b + 3c) * x^2 + (13a + b  7c) * x + (5a  10b + 2c) = 0x^2 + 2x  5
6a + 2b + 3c = 0
13a + b  7c = 2
5a  10b + 2c = 5
6a + 2b + 3c + 2 * (5a  10b + 2c) + 13a + b  7c = 0 + 2 * (5) + 2
6a  10a + 13a + 2b  20b + b + 3c + 4c  7c = 10 + 2
9a  17b + 0c = 8
9a  17b = 8
9a = 17b  8
a = (17b  8) / 9
7 * (6a + 2b + 3c) + 3 * (13a + b  7c) = 7 * 0 + 3 * 2
42a + 39a + 14b + 3b + 21c  21c = 0 + 6
81a + 17b = 6
81 * (1/9) * (17b  8) + 17b = 6
9 * (17b  8) + 17b = 6
9 * 17b + 17b  72 = 6
(9 + 1) * 17b = 78
170 * b = 78
85 * b = 39
b = 39/85
a = (17b  8) / 9
a = (17 * 39/85  8) / 9
a = (39/5  8) / 9
a = (39/5  40/5) / 9
a = (1/5) / 9
a = 1/45
6a + 2b + 3c = 0
6/45 + 78/85 + 3c = 0
3c = 6/45  78/85
c = 2/45  26/85
c = (1/5) * (2/9  26/17)
c = (2/5) * (1/9  13/17)
c = (2/5) * (17/153  117/153)
c = (2/5) * (100/153)
c = 200 / (5 * 153)
c = 40 / 153
a = 1/45
b = 39/85
c = 40/153
(1/45) / (x  2) + (39/85) / (3x  1)  (40/153) / (2x + 5) =>
39 / (85 * (3x  1))  1 / (45 * (x  2)  40 / (153 * (2x + 5))