$\displaystyle \frac{2}{6x^2} + \frac{4}{9x^3} $

I need a common denominator?

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- Mar 20th 2011, 03:36 PMreallylongnicknamerational exp - simplify
$\displaystyle \frac{2}{6x^2} + \frac{4}{9x^3} $

I need a common denominator? - Mar 20th 2011, 03:50 PMpickslides
Try $\displaystyle \displaystyle 6x^2 \times 9x^3$

Or find the lowest common mulitple of the 2. Maybe $\displaystyle \displaystyle 18x^3$ - Mar 20th 2011, 04:05 PMreallylongnickname
$\displaystyle \frac{18}{54x^5}+\frac{24}{54x^5} = \frac{42}{54x^5} $

How's this look? - Mar 20th 2011, 04:23 PMpickslides
That's a good start but its not quite correct.

$\displaystyle \displaystyle \frac{2}{6x^2}+\frac{4}{9x^3} $

$\displaystyle \displaystyle \frac{2}{6x^2}\times \frac{9x^3}{9x^3}+\frac{4}{9x^3}\times \frac{6x^2}{6x^2} $

$\displaystyle \displaystyle \frac{\dots}{54x^5}+\frac{\dots}{54x^5} $ - Mar 20th 2011, 04:43 PMreallylongnickname
$\displaystyle \frac{18x^3}{54x^5}+\frac{24x^2}{54x^5} = \frac{42x^5}{54x^5} = \frac{42}{54}$

- Mar 20th 2011, 04:46 PMe^(i*pi)
You're not done cancelling yet. Recall your six times table

You're on the right track though - Mar 20th 2011, 05:08 PMreallylongnickname
Oh. $\displaystyle \frac{7}{9}$

- Mar 20th 2011, 05:11 PMpickslides
- Mar 20th 2011, 06:45 PMreallylongnickname
Is this the final answer?

$\displaystyle = \frac{18x^3 + 24x^2}{54x^5}$ - Mar 20th 2011, 06:53 PMpickslides
- Mar 20th 2011, 07:07 PMProve It
- Mar 21st 2011, 04:26 AMHallsofIvy
In fact, it would have been better to use $\displaystyle 18x^3$ as your common denominator rather than $\displaystyle 18x^5$.

- Mar 21st 2011, 05:21 AMProve It
Or even better still, note that $\displaystyle \displaystyle \frac{2}{6x^2} = \frac{1}{3x^2}$, then your LCD is $\displaystyle \displaystyle 9x^3$...