Victoria B. answered 08/24/12
Let's Work It Out Together!
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
the equation is undefined at x = 4, and x = -4
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.
Dale B.You can't solve unless there is an = sign somewhere. The other answers help you SIMPLIFY the expression
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.
as I said x cannot equal 4 or -4, since both make the original denominator equal to 0.
The question is incomplete. In order to find x, an equation is needed. An equation must have an "=" sign. It would also help if you could clarify if you mean 32/x^2 or 32/x^(2-16).
Marvin makes an excellent point- we need an equation! Since this is an algebra problem and the x-y coordinate system is such a large part of algebra, it would be a valid assumption to equate the given expression to y. Now we need to decide what the form of the expression is, since it isn't clear.
Three possibilites are: 1. 8x + (32/x^2) - 16. (three terms)
2. 8x +32/(x^2 -16). (two terms)
3. (8x+32)/(x^2 - 16). (one term)
Since no parentheses were used in the original expression I think my first possibility is most probable. Therefore, to solve the first possibility I set the expression equal to y. y = 8x + (32/x^2) - 16. Then I graphed the equation to find the solutions for any x or y. We can see of course that x cannot = 0, since that would make the second term undefined. The most noticeable characteristics of the graph are the asymptotes that approach x=0 from the positive and negative directions.
The other two possibilities could be handled in similar fashion.