| Solving by Clearing Functions | Solving a Rational Function | Eliminating Extraneous Solutions | Word Problems | 
|---|---|---|---|
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					  x=1 or x=3					 
					
					 Solve: x + (3/x) = 4 
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					  x=.0268, 3.732					 
					
					 Solve and check for extraneous solutions:  x + (1/(x-4)) = 0    
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					  x=3 or x=4					 
					
					 Solve and eliminate extraneous solutions: x + (12/x) = 7  
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					  80 mL					 
					
					 How much pure acid can be added to 50 mL of a 35% acid solution to produce a mixture that is 75% acid? 
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| 
						
					 
					  x=2 or x=-7					 
					
					 Solve: x + 5 = 14/x  
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					  x=5					 
					
					 Solve and check for extraneous solutions: ((x-3)/x) - (3/(x+1)) + (3/(x^2+x)) = 0  
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					  x=-3.1 or x=0.661 or x=2.439					 
					
					 Solve and eliminate extraneous solutions: x^2 + (5/x) = 8  
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					  56.57 m					 
					
					 What is the perimeter of a rectangle with an area of 200 square meters? Find the least perimeter.  
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| 
						
					 
					  x=1/2 or x=-1					 
					
					 Solve: 2 - (1/(x+1)) = (1/(x^2+x)) 
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					  no solution					 
					
					 Solve and eliminate extraneous solutions: (3/(x+2)) + (6/(x^2 +2x)) = ((3-x)/x) 
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					  x=-1/3					 
					
					 Solve and eliminate extraneous solutions: (3x/(x+5)) + (1/(x-2)) = (7/(x^2+3x-10))  
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					  169.12 mL					 
					
					 How much pure acid can be added to 125 mL of a 60% acid solution to produce a mixture that is 83% acid?  
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