Candice S.

asked • 03/10/16

could someone please help me with math?

Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box.

3x+5/9x2-25

Rational expression in lowest terms
 
so wouldn't i have to put x+5 in parenthesis so it would be 3(x+5)/9(x+5)(x-5) so i would have to cancel out x+5 and i hve 3/9(x+5) and then reduce 3/9 to 1/3(x+5) or am i wrong? 

1 Expert Answer

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Michael J. answered • 03/10/16

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The denominator is a difference of perfect squares.
 
(3x + 5) / [(3x + 5)(3x - 5)]
 
 
The (3x + 5) factors cancel each other out, leaving only
 
1 / (3x - 5)         as your answer.
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Andrew M.

As Michael J said,
your answer is 1/(3x-5)
 
You also need to note the restrictions on the variable.
Since we cannot divide by zero then, from our
original equation of (3x+5)/(9x2-25) we set
the denominator equal to zero to determine what
values of x are prohibited.
 
9x2 -25 = 0
As Michael J. said, this is a difference of two squares
(3x)2 - 52 = 0
 
Note that a2-b2 = (a-b)(a+b)
so this factors to
(3x-5)(3x+5)
 
If either 3x-5=0 or 3x+5=0
then we are dividing by 0 which is undefined
3x-5=0            3x+5=0
3x=5               3x=-5
x=5/3              x=-5/3
 
The restrictions on your variable are
x ≠ 5/3,  x ≠ -5/3
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03/10/16

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