Rational Expressions

by Anthony
(Meriwether)




1. Find all numbers for which the rational expression is undefined...

5/v-6


2. Divide and simplify...

f+4/f-1 divided by 7f+28/f-6


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Rational Expressions

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Jul 02, 2010
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by: Karin

1. Find all numbers for which the rational number is undefined. 5/v-6

A rational number is undefined when the denominator is 0. Therefore, in this rational expression, if we substituted 6 for v, we would end up with 0 in the denominator. If v = 6, the rational number will be undefined.


2. Divide and simplify:
( f + 4/f-1) / (7f+28/f-6)

Remember that when you divide rational expressions, you actually multiply by the reciprocal.

Therefore, we would rewrite this expression as:
f + 4 f-6
------ * ------
f-1 7f + 28

Now we multiply:

f + 4 f-6 (f+4) (f-6)
------ * ------ = ----------
f-1 7f + 28 (f-1) 7(f+4)

**I factored 7f + 28, by factoring out the 7. When you divide both terms by 7, you end up with:
7 (f+4).

Now we have:
(f+4) (f-6) f-6
------------ = -----
(f-1) 7(f+4) 7(f-1)

Since (f=4) is in the numerator and denominator, we can simplify those terms to 1. We are left with f-6 in the numerator and 7(f-1) in the denominator.

I hope this helps,
Karin

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