SOLUTION: Please show me how to find the least common denominator on my homework question. thank you t^27t+12, t^2-4t, t. The choices are. what is the answer and how do I go about fi

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please show me how to find the least common denominator on my homework question. thank you t^27t+12, t^2-4t, t. The choices are. what is the answer and how do I go about fi      Log On


   

Question 77110: Please show me how to find the least common denominator on my homework question. thank you
t^27t+12, t^2-4t, t.
The choices are. what is the answer and how do I go about finding the answer?
A.) t(t-3)(t-4) B.) t(t+3)(t-4)
C.) t^2(t-3)(t-4) D.) t^2(t+3)(t-4)
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!


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