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# Write as a single fraction?

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144
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1/b + 1/b^2 + 1/b^3

Guest Jun 6, 2017

#1
+1493
+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
Sort:

#1
+1493
+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

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