Solution 2.1:8c - Revision history

Tek at 12:41, 23 September 2008

2008-09-23T12:41:05Z

←Older revision		Revision as of 12:41, 23 September 2008
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-	When we come across large and complicated expressions, we have to work step by step;	+	When we come across large and complicated expressions, we have to work step by step; as a first goal, we can multiply the top and bottom of the fraction

-	~~as a first goal, we can multiply the top and bottom of the fraction~~	+	{{Displayed math\|\|<math>\frac{1}{1+\dfrac{1}{1+x}}</math>}}

		+	by <math>1+x</math>, so as to reduce it to an expression having one fraction sign

-	~~<math>\frac~~{1}{~~1+\frac{1}{1+x}}</~~math>	+	{{Displayed math\|\|<math>\begin{align}
-		+	\frac{1}{1+\dfrac{1}{1+\dfrac{1}{1+x}}}
-		+	&= \frac{1}{1+\dfrac{1}{1+\dfrac{1}{1+x}}\cdot\dfrac{1+x}{1+x}}\\[8pt]
-	by	+	&= \frac{1}{1+\dfrac{1+x}{\Bigl(1+\dfrac{1}{1+x}\Bigr)(1+x)}}\\[8pt]
-	~~<math>1+x</math>, so as to reduce it to an expression having one fraction sign:~~	+	&= \frac{1}{1+\dfrac{1+x}{1+x+\dfrac{1+x}{1+x}}}\\[8pt]
-		+	&= \frac{1}{1+\dfrac{1+x}{1+x+1}}\\[8pt]
-		+	&= \frac{1}{1+\dfrac{x+1}{x+2}}\,\textrm{.}
-	<math>\begin{align}	+	\end{align}</math>}}
-	& \frac{1}{1+\~~frac~~{1}{1+\~~frac~~{1}{1+x}}}=\frac{1}{1+\~~frac~~{1}{1+\~~frac~~{1}{1+x}}\~~centerdot~~ \~~frac~~{1+x}{1+x}}=\frac{1}{1+\~~frac~~{1+x}{\~~left~~( 1+\~~frac~~{1}{1+x} \~~right~~)~~\left~~( 1+x ~~\right~~)}} \\	+
-	~~& \\~~	+
-	& =\frac{1}{1+\~~frac~~{1+x}{1+x+\~~frac~~{1+x}{1+x}}}=\frac{1}{1+\~~frac~~{1+x}{1+x+1}}=\frac{1}{1+\~~frac~~{x+1}{x+2}} \\	+
-	\end{align}</math>	+
-		+

	The next step is to multiply the top and bottom of our new expression by		The next step is to multiply the top and bottom of our new expression by
-	<math>x+2</math>,	+	<math>x+2</math>, so as to obtain the final answer,
-	so as to obtain the final answer,	+
-		+

-	<math>\begin{align}	+	{{Displayed math\|\|<math>\begin{align}
-	& \frac{1}{1+\~~frac~~{x+1}{x+2}}\~~centerdot~~ \frac{x+2}{x+2}=\frac{x+2}{\~~left~~( 1+\~~frac~~{x+1}{x+2} \~~right~~)~~\left~~( x+2 ~~\right~~)}=\frac{x+2}{x+2+\~~frac~~{x+1}{x+2}~~\left~~( x+2 ~~\right~~)} \\	+	\frac{1}{1+\dfrac{x+1}{x+2}}\cdot\frac{x+2}{x+2}
-	& \\	+	&= \frac{x+2}{\Bigl(1+\dfrac{x+1}{x+2}\Bigr)(x+2)}\\[8pt]
-	& \frac{x+2}{x+2+x+1}=\frac{x+2}{2x+3} \\	+	&= \frac{x+2}{x+2+\dfrac{x+1}{x+2}(x+2)}\\[8pt]
-	~~& \\~~	+	&= \frac{x+2}{x+2+x+1}\\[8pt]
-	\end{align}</math>	+	&= \frac{x+2}{2x+3}\,\textrm{.}
		+	\end{align}</math>}}

Ian at 13:52, 16 September 2008

2008-09-16T13:52:56Z

←Older revision		Revision as of 13:52, 16 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	When we come across large and complicated expressions, we have to work step by step;
-	<~~center~~> ~~[[Image:2_1_8c-~~1~~(2).gif]]~~ </~~center~~>	+
-	{{~~NAVCONTENT_STOP~~}}	+	as a first goal, we can multiply the top and bottom of the fraction
-	{{~~NAVCONTENT_START~~}}	+
-	<~~center~~> ~~[[Image:2_1_8c-~~2~~(2).gif]]~~ </~~center~~>	+
-	{{~~NAVCONTENT_STOP~~}}	+	<math>\frac{1}{1+\frac{1}{1+x}}</math>
		+
		+
		+	by
		+	<math>1+x</math>, so as to reduce it to an expression having one fraction sign:
		+
		+
		+	<math>\begin{align}
		+	& \frac{1}{1+\frac{1}{1+\frac{1}{1+x}}}=\frac{1}{1+\frac{1}{1+\frac{1}{1+x}}\centerdot \frac{1+x}{1+x}}=\frac{1}{1+\frac{1+x}{\left( 1+\frac{1}{1+x} \right)\left( 1+x \right)}} \\
		+	& \\
		+	& =\frac{1}{1+\frac{1+x}{1+x+\frac{1+x}{1+x}}}=\frac{1}{1+\frac{1+x}{1+x+1}}=\frac{1}{1+\frac{x+1}{x+2}} \\
		+	\end{align}</math>
		+
		+
		+	The next step is to multiply the top and bottom of our new expression by
		+	<math>x+2</math>,
		+	so as to obtain the final answer,
		+
		+
		+	<math>\begin{align}
		+	& \frac{1}{1+\frac{x+1}{x+2}}\centerdot \frac{x+2}{x+2}=\frac{x+2}{\left( 1+\frac{x+1}{x+2} \right)\left( x+2 \right)}=\frac{x+2}{x+2+\frac{x+1}{x+2}\left( x+2 \right)} \\
		+	& \\
		+	& \frac{x+2}{x+2+x+1}=\frac{x+2}{2x+3} \\
		+	& \\
		+	\end{align}</math>

Tekbot: Lösning 2.1:8c moved to Solution 2.1:8c: Robot: moved page

2008-09-09T08:42:03Z

Lösning 2.1:8c moved to Solution 2.1:8c: Robot: moved page

←Older revision

Revision as of 08:42, 9 September 2008

Tekbot: Robot: Automated text replacement (-[[Bild: +[[Image:)

2008-08-21T06:38:09Z

Robot: Automated text replacement (-[[Bild: +[[Image:)

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Lina at 11:25, 31 March 2008

2008-03-31T11:25:05Z

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Lina: Ny sida: {{NAVCONTENT_START}} Bild:2_1_8c-1(2).gif {{NAVCONTENT_STOP}}

2008-03-31T11:24:21Z

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