Solution 2.2:3a - Revision history

Tek at 07:03, 24 September 2008

Tek — Wed, 24 Sep 2008 07:03:10 GMT

←Older revision		Revision as of 07:03, 24 September 2008
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-	We multiply the top and bottom of the terms on the left-hand side by appropriate factors so that they have the same common denominator, in the following way:	+	We multiply the top and bottom of the terms on the left-hand side by appropriate factors so that they have the same common denominator, in the following way,

		+	{{Displayed math\|\|<math>\frac{x+3}{x-3}\cdot \frac{x-2}{x-2}-\frac{x+5}{x-2}\cdot \frac{x-3}{x-3}=0\,\textrm{.}</math>}}

-	~~<math>\frac{x+3}{x-3}\centerdot \frac{x-2}{x-2}-\frac{x+5}{x-2}\centerdot \frac{x-3}{x-3}=0</math>~~	+	Now, the numerators can be subtracted,

		+	{{Displayed math\|\|<math>\frac{(x+3)(x-2)-(x+5)(x-3 )}{(x-2)(x-3)}=0\,\textrm{.}</math>}}

-	~~Now, the numerators can be subtracted:~~	+	Expand the brackets in the numerator,
-		+
-		+
-	~~<math>\frac{\left( x+3 \right)\left( x-2 \right)-\left( x+5 \right)\left( x-3 \right)}{\left( x-2 \right)\left( x-3 \right)}=0</math>~~	+
-		+
-		+
-	Expand the brackets in the numerator	+
-		+
-		+
-	~~<math>\frac{x^{2}-2x+3x-6-\left( x^{2}-3x+5x-15 \right)}{\left( x-2 \right)\left( x-3 \right)}=0</math>~~	+

		+	{{Displayed math\|\|<math>\frac{x^{2}-2x+3x-6-(x^{2}-3x+5x-15)}{(x-2)(x-3)}=0</math>}}

	and simplify		and simplify

-		+	{{Displayed math\|\|<math>\frac{-x+9}{(x-2)(x-3)}=0\,\textrm{.}</math>}}
-	<math>\frac{-x+9}{~~\left~~( x-2 ~~\right~~)~~\left~~( x-3 ~~\right~~)}=0</math>	+
-		+

	The left-hand side will be zero only when its numerator is zero (provided the denominator is not also zero), which gives us that the equation's solutions are given by the solutions to		The left-hand side will be zero only when its numerator is zero (provided the denominator is not also zero), which gives us that the equation's solutions are given by the solutions to

		+	{{Displayed math\|\|<math>-x+9=0\,</math>,}}

-	~~<math>-x+9=0</math>~~	+	i.e. <math>x=9</math>.
-		+
-	i.e.	+
-	<math>x=9</math>.	+
-		+
-	~~Substituting~~	+
-	~~<math>x=9</math>~~	+
-	~~into the original equation shows that we have calculated correctly:~~	+

		+	Substituting <math>x=9</math> into the original equation shows that we have calculated correctly,

-	<math>\text{LHS}=\frac{9+3}{9-3}-\frac{9+5}{9-2}=\frac{12}{6}-\frac{14}{7}=2-2=0=\text{RHS}</math>	+	{{Displayed math\|\|<math>\text{LHS}=\frac{9+3}{9-3}-\frac{9+5}{9-2}=\frac{12}{6}-\frac{14}{7}=2-2=0=\text{RHS.}</math>}}

Ian at 14:06, 17 September 2008

Ian — Wed, 17 Sep 2008 14:06:26 GMT

←Older revision		Revision as of 14:06, 17 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	We multiply the top and bottom of the terms on the left-hand side by appropriate factors so that they have the same common denominator, in the following way:
-	<~~center~~> ~~[[Image~~:~~2_2_3a~~-1(2)~~.gif]]~~ </~~center~~>	+
-	{{~~NAVCONTENT_STOP~~}}	+
-	{~~{NAVCONTENT_START~~}}	+	<math>\frac{x+3}{x-3}\centerdot \frac{x-2}{x-2}-\frac{x+5}{x-2}\centerdot \frac{x-3}{x-3}=0</math>
-	<~~center~~> ~~[[Image:2_2_3a~~-2(2).~~gif]]~~ </~~center~~>	+
-	{{~~NAVCONTENT_STOP~~}}	+
		+	Now, the numerators can be subtracted:
		+
		+
		+	<math>\frac{\left( x+3 \right)\left( x-2 \right)-\left( x+5 \right)\left( x-3 \right)}{\left( x-2 \right)\left( x-3 \right)}=0</math>
		+
		+
		+	Expand the brackets in the numerator
		+
		+
		+	<math>\frac{x^{2}-2x+3x-6-\left( x^{2}-3x+5x-15 \right)}{\left( x-2 \right)\left( x-3 \right)}=0</math>
		+
		+
		+	and simplify
		+
		+
		+	<math>\frac{-x+9}{\left( x-2 \right)\left( x-3 \right)}=0</math>
		+
		+
		+	The left-hand side will be zero only when its numerator is zero (provided the denominator is not also zero), which gives us that the equation's solutions are given by the solutions to
		+
		+
		+	<math>-x+9=0</math>
		+
		+	i.e.
		+	<math>x=9</math>.
		+
		+	Substituting
		+	<math>x=9</math>
		+	into the original equation shows that we have calculated correctly:
		+
		+
		+	<math>\text{LHS}=\frac{9+3}{9-3}-\frac{9+5}{9-2}=\frac{12}{6}-\frac{14}{7}=2-2=0=\text{RHS}</math>

Tekbot: Lösning 2.2:3a moved to Solution 2.2:3a: Robot: moved page

Tekbot — Tue, 09 Sep 2008 08:45:03 GMT

Lösning 2.2:3a moved to Solution 2.2:3a: Robot: moved page

←Older revision

Revision as of 08:45, 9 September 2008

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

Tekbot — Thu, 21 Aug 2008 06:39:39 GMT

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

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Lina at 14:36, 31 March 2008

Lina — Mon, 31 Mar 2008 14:36:12 GMT

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Lina — Mon, 31 Mar 2008 14:35:24 GMT

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