004 Sample Final A, Problem 10 - Revision history

Kayla Murray at 23:43, 4 May 2015

2015-05-04T23:43:52Z

2015-05-04T23:33:59Z

2015-05-04T23:20:15Z

2015-04-28T22:42:35Z

Created page with "<span class="exam"> Decompose into separate partial fractions. <math>\frac{6x^2 + 27x + 31}{(x + 3)^2(x-1)}</math>"

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<span class="exam"> Decompose into separate partial fractions.      <math>\frac{6x^2 + 27x + 31}{(x + 3)^2(x-1)}</math>

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 ! Step 3:
 |-
+|If we set <math>x=1</math> in the above equation, we get <math>16A=64</math> and <math>A=4</math>.
 |-
+|If we set <math>x=-3</math> in the above equation, we get <math>-4C=4</math> and <math>C=-1</math>.
 |}
@@ Line 46: / Line 42: @@
 ! Step 4:
 |-
+|In the equation <math>6x^2+27x+31=A(x+3)^2+B(x+3)(x-1)+C(x-1)</math>, we compare the constant terms of both sides. We must have
 |-
+|<math>9A-3B-C=31</math>. Substituting <math>A=4</math> and <math>C=-1</math>, we get <math>B=2</math>.
 |-
+|Thus, the partial fraction decomposition is <math>\frac{4}{x-1}+\frac{2}{x+3}+\frac{-1}{{(x+3)}^2}</math>
 |}
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 ! Final Answer:
 |-
+|<math>\frac{4}{x-1}+\frac{2}{x+3}+\frac{-1}{{(x+3)}^2}</math>
 |}
 [[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

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 ! Foundations
 |-
+|1) What is the form of the partial fraction decomposition of <math>\frac{3x-37}{(x+1)(x-4)}</math>?
 |-
 |Answer:
 |-
+|1) <math>\frac{A}{x+1}+\frac{B}{x-4}</math>
 |}
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 ! Step 1:
 |-
+|We set <math>\frac{6x^2 + 27x + 31}{(x + 3)^2(x-1)}=\frac{A}{x-1}+\frac{B}{x+3}+\frac{C}{{(x+3)}^2}</math>.
 |}
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 ! Step 2:
 |-
+|Multiplying both sides of the equation by <math>(x + 3)^2(x-1)</math>, we get
 |}

← Older revision		Revision as of 23:20, 4 May 2015
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	<span class="exam"> Decompose into separate partial fractions.      <math>\frac{6x^2 + 27x + 31}{(x + 3)^2(x-1)}</math>		<span class="exam"> Decompose into separate partial fractions.      <math>\frac{6x^2 + 27x + 31}{(x + 3)^2(x-1)}</math>
		+	{\| class="mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Foundations
		+	\|-
		+	\|
		+	\|-
		+	\|Answer:
		+	\|-
		+	\|
		+	\|}
		+
		+
		+	Solution:
		+
		+	{\| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 1:
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|}
		+
		+	{\|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 2:
		+	\|-
		+	\|
		+	\|}
		+
		+	{\|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 3:
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|}
		+
		+	{\|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 4:
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|}
		+
		+	{\|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Final Answer:
		+	\|-
		+	\|
		+	\|}
		+
		+	[[004 Sample Final A\|<u>'''Return to Sample Exam</u>''']]