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1/b + 1/b^2 + 1/b^3

Guest Jun 6, 2017

Best Answer 

 #1
avatar+2248 
+1

 

Simplifying these terms requires one to place them in a common denominator. To do this, we must find the LCD, or lowest common denominator of the terms. In this case, \(b^3\) is the LCD.

 

Let's worry about each term individually. Let's convert \(\frac{1}{b}\) so that its denominator is \(b^3\):

 

\(\frac{1}{b}*\frac{b^2}{b^2}\) Multiply both the numerator and denominator by \(b^2\)
\(\frac{b^2}{b^3}\) This term has a denominator of b^3 now. 
   

 

Let's do the other term now:
 

\(\frac{1}{b^2}*\frac{b}{b}\) Multiply the numerator and denominator by \(b\)
\(\frac{b}{b^3}\)  
   

 

Of course the other term is converted already in its desired form, so we need not worry about the third one. Let's add the fractions together now:

 

\(\frac{b^2}{b^3}+\frac{b}{b^3}+\frac{1}{b^3}=\frac{b^2+b+1}{b^3}\)

 

This answer cannot be simplified further. 

TheXSquaredFactor  Jun 6, 2017
 #1
avatar+2248 
+1
Best Answer

 

Simplifying these terms requires one to place them in a common denominator. To do this, we must find the LCD, or lowest common denominator of the terms. In this case, \(b^3\) is the LCD.

 

Let's worry about each term individually. Let's convert \(\frac{1}{b}\) so that its denominator is \(b^3\):

 

\(\frac{1}{b}*\frac{b^2}{b^2}\) Multiply both the numerator and denominator by \(b^2\)
\(\frac{b^2}{b^3}\) This term has a denominator of b^3 now. 
   

 

Let's do the other term now:
 

\(\frac{1}{b^2}*\frac{b}{b}\) Multiply the numerator and denominator by \(b\)
\(\frac{b}{b^3}\)  
   

 

Of course the other term is converted already in its desired form, so we need not worry about the third one. Let's add the fractions together now:

 

\(\frac{b^2}{b^3}+\frac{b}{b^3}+\frac{1}{b^3}=\frac{b^2+b+1}{b^3}\)

 

This answer cannot be simplified further. 

TheXSquaredFactor  Jun 6, 2017

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