Question 77110
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Please show me how to find the least common denominator on my homework
question.  thank you

tē-7t+12, tē-4t, t.

Factor the ones that will factor:

(t-3)(t-4), t(t-4), t

The factor (t-3) appears ONE time in the first expression, (t-3)(t-4)
The factor (t-3) appears ONE time in the second expression, t(t-4)
The factor (t-3) appears NO times in the third expression, t

That's AT MOST ONE time.  So the LCD contains (t-3) ONE time

So far the LCD = (t-3)

The factor (t-4) appears ONE time in the first expression, (t-3)(t-4)
The factor (t-4) appears ONE time in the second expression, t(t-4)
The factor (t-4) appears NO times in the third expression, t

That's AT MOST ONE time.  So the LCD contains (t-4) ONE time

So far the LCD = (t-3)(t-4)

The factor t appears NO time in the first expression, (t-3)(t-4)
The factor t appears ONE time in the second expression, t(t-4)
The factor t appears ONE times in the third expression, t

That's AT MOST ONE time.  So the LCD contains t ONE time

So far the LCD = (t-3)(t-4)t

We've gone through all the factors, so that's it.
It is customary to write the shorter factor first, so you'd probably
want to leave it this way:

LCD = t(t-3)(t+4)

Edwin</pre>