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
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7 Answers By Expert Tutors
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
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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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09/27/19
Joseph M. answered • 09/08/12
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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.
Ana D. answered • 08/26/12
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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
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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
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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)
Prem D. answered • 09/13/19
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8/x-4
Frank L. answered • 08/24/12
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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