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

## 14 Answers By Expert Tutors

Victoria B. answered • 08/24/12

Let's Work It Out Together!

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.

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.09/27/19

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.

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.

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)

Cheryl P. answered • 16d

Experienced tutor in algebra, geometry, & standardized testing

**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

__8x + 32__

x^{2} - 16

**FACTOR NUMERATOR & DENOMINATOR**

__ 8 (x + 4)____

(x - 4) (x + 4)

**CROSS OUT MATCHING FACTORS**

__ 8 (____x + 4____)__

(x - 4) (~~x + 4~~)

**FINAL ANSWER**

__ 8___

x - 4

**THE DENOMINATOR CANNOT EQUAL ZERO**

**LET EACH FACTOR IN THE ORIGINAL DENOMINATOR EQUAL ZERO**

**[IN THIS CASE, I JUST GO AHEAD & INSERT THE INEQUALITY SIGN SO I WON'T FORGET]**

**[IF YOU USE THE EQUALS SIGN, DON'T FORGET TO DELETE THE ANSWER FROM ANY SOLUTION AT THE END]**

x - 4 ≠ 0

x - 4 + 4 ≠ 0 + 4

x ≠ 4

x + 4 ≠ 0

x + 4 - 4 ≠ 0 - 4

x ≠ -4

**THEREFORE, X CANNOT EQUAL 4 OR -4**

Sam Z. answered • 01/10/23

Experienced Math Tutor Grades 1-12: College Math Major

First you need to simplify the equation and then find the domain (where x is "allowed") and range (where y is "allowed").

- Start with the numerator: you can factor out an 8 to get 8x+32 = 8(x+4).
- Now the denominator: this is a difference of squares
- this is the form of x^2 - a^2 = (x+a)(x-a), where a is any real number
- so in this example a = 4: x^2 - 16 = x^2 - (4^2) = (x+4)(x-4)
- Finally we we can cancel: [8(x+4)]/[(x+4)(x-4)] = 8/(x-4)
- Domain and Range
- Domain: when x = 4, f(x) = 8/0, which is undefined (not "allowed"), so your domain is

(-∞,4)∪(4,∞)

- Range: y will never = 0, so your range is

(-∞,0)∪(0,∞)

Maryellen P. answered • 02/01/22

Retired High School Math Teacher

Solve 8x+32/x^-16.

In this problem, there is no equal sign. This means that we will not solve for a value for x, but we will simplify the expression.

Simplifying this rational expression is similar to simplifying fractions- look for common factors.

The numerator can be factored 8(x+4)

The denominator can be factored (x+4)(x-4)

The common factor is (x+4)

Simplifying results in 8/(x-4) This is the simplified expression.

It is also important to note, that since there is a variable in the denominator, we need to put restrictions on the variable so that the denominator does not equal 0. The restrictions on the variable are that x cannot equal 4 or -4.

Stephen C. answered • 01/13/22

SAT Math, Algebra, Trig, PreCalc Tutor

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.)

David B. answered • 08/28/21

Former Math Teacher and Experienced and Patient Tutor

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)/(x^{2}-16) or 8x+32/x^{2}-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(x^{3}-2x^{2}+4)/x^{2} as long as x is not 0.

^{ }

^{ }

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