how do you solve 8x+32/x^2-16

Question

it is radicals what if x has no value and results in denominator with a value of 0

and is not undefined

 

Answer 1

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)

 

                                                 

 

Answer 2

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.

Answer 3

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.

Answer 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.

Answer 5

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.

Answer 6

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)

Answer 7

A slightly different approach:

First, lets assume that the intended problem is to solve the equation:

[ (8x + 32) / (x^2 - 16) ] = 0

That is, we want to find one or more values for x that make the equation true.

For the equation to be true, the numerator of the fraction, (8x + 32), must be 0.

If 8x + 32 is 0, then x must be -4, and our solution is x = -4.

But wait: if x is -4, then the denominator of the fraction, (x^2 - 16), is zero, so that the fraction is undefined.

This is a contradiction, so there are no real solutions to the equation.

(Plug in various values for x, if you need more convincing.)

Answer 8

Where is the equation if we are solving for x?

Maybe we are just supposed to simplify the expression?

Also, is the expression (8x+32)/(x²-16) or 8x+32/x²-16?

If it is the first then 8/(x-4) would be the correct simplification as long as x does not equal 4 or -4.

If it is the second then the correct simplification would be 8(x³-2x²+4)/x² as long as x is not 0.

Answer 9

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)

Answer 10

8/x-4

Answer 11

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