SOLUTION: what are the non-permissible values for the rational expression x^2-4/y^2-4 a. y=0 and y=1 b. y=4 and y=-4 c. y=0 and y=3 d. y=2 and y=-2

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Question 89391: what are the non-permissible values for the rational expression x^2-4/y^2-4
a. y=0 and y=1
b. y=4 and y=-4
c. y=0 and y=3
d. y=2 and y=-2
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
You have written the problem a little wrong. What you wrote would be interpreted by the rules
of algebra as:
.

.
Note that the -4 is not in the denominator. What you meant to write was:
.

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The reason for this is that the rules of algebraic notation tell you to go through a problem
from left to right and do all the multiplications and divisions first. Then you return and
from left to right in sequence you do all the additions and subtractions. So the way you
wrote the problem in going from left to right doing in sequence the multiplications
and divisions you would first divide -4 by y^2 to get . That completes the
multiplications and divisions and the problem is then:
.

.
and you can see why the problem is not what you intended. You intended the -4 to be in the
denominator also, and you can indicate that by putting the entire denominator in parentheses
as in (y^2 - 4)
.
Anyhow, back to the problem you did intend:
.

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Factor the denominator . This falls into the factoring form:
.

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In this case a = y and b = 2 so that the factored form is (y - 2)*(y + 2). So the problem
becomes:
.

.
Now you can tell that y cannot be +2 and y also cannot be -2 because if y had either of
those values one of the factors in the denominator would be zero, making the entire
denominator zero and in algebra a division by zero is not allowed. Therefore, answer d
is the correct answer.
.
Hope this helps you to gain a little more understanding of writing algebraic terms in
a line (doing multiplications and divisions first) and then an understanding of this problem.
.
Cheers!