Tracy D.

asked • 08/24/12

how 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

 

Joseph M.

as I said x cannot equal 4 or -4, since both make the original denominator equal to 0.

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09/09/12

Marvin F.

tutor

The question is incomplete.  In order to find x, an equation is needed.  An equation must have an "=" sign.  It would also help if you could clarify if you mean 32/x^2 or 32/x^(2-16).

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05/20/13

Thomas G.

tutor

Marvin makes an excellent point- we need an equation! Since this is an algebra problem and the x-y coordinate system is such a large part of algebra, it would be a valid assumption to equate the given expression to y.  Now we need to decide what the form of the expression is, since it isn't clear.

 Three possibilites are: 1. 8x + (32/x^2) - 16. (three terms)

                                  2. 8x +32/(x^2 -16). (two terms)

                                  3. (8x+32)/(x^2 - 16). (one term)

Since no parentheses were used in the original expression I think my first possibility is most probable.  Therefore, to solve the first possibility I set the expression equal to y.  y = 8x + (32/x^2) - 16.  Then I graphed the equation to find the solutions for any x or y. We can see of course that x cannot = 0, since that would make the second term undefined. The most noticeable characteristics of the graph are the asymptotes that approach x=0 from the positive and negative directions.

The other two possibilities could be handled in similar fashion.

 

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05/27/13

7 Answers By Expert Tutors

By:

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)

 

                                                 

 

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Tracy D.

what if variable has no value and results in a denominator of 0

 

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08/24/12

Joseph M.

the equation is undefined at x = 4, and x = -4

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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.  

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09/09/12

Dale B.

You can't solve unless there is an = sign somewhere. The other answers help you SIMPLIFY the expression
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07/17/19

Alex L.

tutor
Factoring this problem to 8(x+4)/((x+4)(x-4)) is the first step. Next you should recognize that you have an (x+4) factor in the numerator and the denominator. This causes there to be a hole at x= - 4. Next you notice that you still have a factor of (x-4) in the denominator that causes a vertical asymptote at x=4. This graph will look exactly like the graph of 8/(x-4) except it will have a hole at x=-4 or at the coordinate (- 4, -0.5) there will be a hole with no value. As x approaches 4 from the negative side, y will approach negative infinity and as x approaches 4 from the positive side y will approach positive infinity. As x approaches positive and negative infinity, y will simply approach zero.
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24d

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.

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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.

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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)

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Prem D. answered • 09/13/19

Experienced High School Tutor

8/x-4

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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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