WyzAnt.comit is radicals what if x has no value and results in denominator with a value of 0
and is not undefined
how do you solve 8x+32/x^2-16
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6 Answers
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)
Comments
what if variable has no value and results in a denominator of 0
- Tracy D. from Greencastle, IN 8/24/2012
the equation is undefined at x = 4, and x = -4
- Joseph M. 9/9/2012just 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.
- Joseph M. 9/9/2012Everthing 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
Answer = 8/(x-4)
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
Comments
as I said x cannot equal 4 or -4, since both make the original denominator equal to 0.
- Joseph M. 9/9/2012