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# 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

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

9/9/2012

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)

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

8/24/2012

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

9/9/2012

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.

9/9/2012

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.

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.

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.

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

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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