Express the rational function as a sum or difference of two simpler rational expressions.   shouldnt it be x^2 not just x above the red line?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 55E
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Express the rational function as a sum or difference of two simpler rational expressions.

 

shouldnt it be x^2 not just x above the red line?

 

 

189.
x*(x – 1)
Transcribed Image Text:189. x*(x – 1)
1
q2 (r – 1)
Decompose into partial fractions
1.
A
В
C
r2 (x – 1)
1
To solve for A, B and C, multiply both sides by the LCD to clear fractions
1= Ar (r – 1) + B (x – 1) + Ca?
Apply the distributive property
1 = Ax? – Ax + Bx – B + Cx?
Combine like terms
1= (Ar? + Ca?) + (- Ar + Bx) – B
1 = (A+ C) r? + (-A+ B)x – B
Equate the coefficients to obtain a system of linear equations
1 = (A + C)x? +(-A+ B)x + (-B)
A +C = 0
— А+ В %— 0
— В %3 1
Solve the system of linear equations
A = -1, B = -1, C = 1
Replacing A, B and C into the partial fraction decomposition
1
A
В
т2 (х — 1)
1
1
r2 (x – 1)
.2
x - 1
LT
1
+
Transcribed Image Text:1 q2 (r – 1) Decompose into partial fractions 1. A В C r2 (x – 1) 1 To solve for A, B and C, multiply both sides by the LCD to clear fractions 1= Ar (r – 1) + B (x – 1) + Ca? Apply the distributive property 1 = Ax? – Ax + Bx – B + Cx? Combine like terms 1= (Ar? + Ca?) + (- Ar + Bx) – B 1 = (A+ C) r? + (-A+ B)x – B Equate the coefficients to obtain a system of linear equations 1 = (A + C)x? +(-A+ B)x + (-B) A +C = 0 — А+ В %— 0 — В %3 1 Solve the system of linear equations A = -1, B = -1, C = 1 Replacing A, B and C into the partial fraction decomposition 1 A В т2 (х — 1) 1 1 r2 (x – 1) .2 x - 1 LT 1 +
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