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

## 9 Answers By Expert Tutors

Solve: 8x + 32 / x^{2} - 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/x^{2}-16 factor both the denominator x^{2}-16 and the numerator 8x+32 as follows:

8x+32=8(x+4)

x^{2}-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