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explain why multiplying both sides of a rational equation by the LCD eliminates all of the denominators

 Mar 6, 2019
 #1
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Let's take an example

 

5 / (x - 1)    +  3 / (x + 2 )   =  5

 

The LCM  is  (x - 1) ( x + 2)

 

So

 

5 (x - 1) ( x + 2) / (x - 1)  + 3(x - 1) ( x + 2) / (x + 2)   =  5(x - 1) ( x + 2)

 

5(x + 2)  + 3(x - 1)  = 5(x - 1) ( x + 2)

 

So...multiplying by the LCM    "cancels out" the denominators

 

 

cool cool cool

 Mar 6, 2019
 #2
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presumably because the LCD would be factors of everything on both sides, meaning all the denominators are "canceled"?

 Mar 6, 2019

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