
Tracy D.
asked 08/24/12how do you solve 8x+32/x^2-16
it is radicals what if x has no value and results in denominator with a value of 0
and is not undefined
9 Answers By Expert Tutors
Victoria B. answered 08/24/12
Let's Work It Out Together!
Solve: 8x + 32 / x2 - 16
First factor out as much as possible.
The numerator can be factored out as: 8(x + 4)
The demoninator can be factored out as: (x + 4) (x - 4)
Now you have 8 (x + 4) / (x + 4) (x - 4)
The (x + 4) in both numerator and demoninator can be eliminated.
What you have left is 8 / (x - 4)
Tracy D.
what if variable has no value and results in a denominator of 0
08/24/12

Joseph M.
the equation is undefined at x = 4, and x = -4
09/09/12

Joseph M.
just because the x+4 in the denominator can be factored out does not mean it does not make the denominator equal to 0: it does. Any number that makes the denominator equal to 0 makes the function undefined, so x cannot equal that number, so in this case x cannot equal 4 or -4.
09/09/12

Dale B.
You can't solve unless there is an = sign somewhere. The other answers help you SIMPLIFY the expression07/17/19

Alex L.
09/27/19

Joseph M. answered 09/08/12
A Former Math Teacher who is Mr. Renaissance!
Everthing said by the other posters here is correct with one addition just as x cannot equal 4, x cannot equal -4, because the original denominator was (x-4)(x+4), and neither factor can equal 0. x-4 = 0, x=4, x+4 = 0, x=-4. There is a little jump or a circle on the graph when x=-4.
Solve (simplify)
8x + 32
x^2 - 16
Step 1: Factor numerator and denominator
8(x+4)__
(x+4)(x-4)
Step 2: Notice (x+4) in both expressions
8(x+4)__
(x+4)(x-4)
Step 3: The (x+4)’s cancel out leaving the simplified expression
___8___
(x-4)
Step 4: In order to find the undefined values, look at the original expression. When x^2 - 16 is 0, then the expression contains 0 in the denominator which by definition is undefined. For x^2 - 16 to equal zero, x must be the square root of 16, which is both 4 and -4, so the expression is undefined when x = 4 or x= -4.

Ana D. answered 08/26/12
Certified Public School Teacher - Middle School Math and French
To solve 8x+32/x2-16 factor both the denominator x2-16 and the numerator 8x+32 as follows:
8x+32=8(x+4)
x2-16= (x+4)(x-4)
Therefore, 8x+32/x2-16=8(x+4)/(x+4)(x-4)
Simplify, by dividing both the numerator and the denominator by the common factor,(x+4)
The final answer is 8/x-4. Solution: All real numbers except x=4, which would render the denominator zero and the fraction undefined.
Thomas G. answered 08/26/12
Tutoring Algebra I & II; Excellent Understanding & Patience
If (8x+32)/ (x^2 -16) is meant, then
factor the numenerator: 8(x+4)
factor the denominator: (x+4)(x-4)
resulting in: 8(x+4)/(x+4)(x-4)
the (x+4) term in numerator and denominator cancel, leaving 8/(x-4).
The solution for x is all real numbers, except x=4.

Herbert N. answered 08/24/12
Effective Tutor for All Mathematics & Economics Subjects Needs
how do you solve 8x+32/x^2-16
To solve this you must use factoring.
Factor 8x+32 = 8(x+4)
Factor X^2-16 = (x-4)(x+4)
Now Divide = 8(x+4)/(x-4)(x+4)
Simplify = (x+4) cancels out
Answer = 8/(x-4)
Odds are you meant to put parentheses in such as (8x+32)/(x^2-16)
then it's a factoring problem = 8(x+4)/(x+4)(x-4). The (x-4)'s cancel leaving
8/(x-4) where x can be any real number except 4 or -4, as that makes the denominator 0 and the expression undefined. You might miss -4 as disallowed if you look only at the expression after cancelling factors.
However, without the parentheses, the problem is
8x + 32/x^2 -16, with 3 terms, and only 1 in fractional form
You could factor out an 8 to get
8(x + 32/x^2 - 16). That's as simple as it gets. But this way, x=0 is the disallowed value that makes the expression undefined.
but the way it's written you really have 3 terms, 8x, 32/x^2 and -16 all added together, which gives
8x-16 + 32/x^2 (in exponential order) you can factor out 8 to get
8(x-2+4/x^2)
Prem D. answered 09/13/19
Experienced High School Tutor
8/x-4

Frank L. answered 08/24/12
I love golf, my dog and teaching;not necessarily in that order!
There are a few ways SET 8x+32/x^2-16=0
Then multiply the equation by x^2 -> 8x^3+32-16x^2=0
Take the derivative (if you know calculus) -> 24x^2-16x=0 and divide by 16 x^2-2/3 x=0
the derivative set to zero give points of zero slope for the equation not the zeros on the x axis You can plot by hand or use a graphing calculator to find the root which is near -1
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Joseph M.
as I said x cannot equal 4 or -4, since both make the original denominator equal to 0.
09/09/12