SOLUTION: Could someone please help me break this down and: find all numbers for which the rational expression is undefined? 4/5w+9. I am having a difficult time understanding how to do this

Algebra ->  Rational-functions -> SOLUTION: Could someone please help me break this down and: find all numbers for which the rational expression is undefined? 4/5w+9. I am having a difficult time understanding how to do this      Log On


   

Question 625882: Could someone please help me break this down and: find all numbers for which the rational expression is undefined? 4/5w+9. I am having a difficult time understanding how to do this. I don't understand the concept of setting the denominator to zero, then performing the functions. Details would be greatly appreciated as I am trying to learn not just get answers. Thank you for your time.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
4%2F%285w%2B9%29
An expression such as this is said to be "undefined" if the denominator is equal to zero.
Why, because when the denominator is zero, you are then, in effect, dividing the numerator by zero and division by zero is "undefined" and thus not permitted.
Thus, you need to find what value(s) of the variable, w, would make the denominator equal zero. One simple way to do this is to set the denominator equal to zero and solve for the variable, w.
5w%2B9+=+0 Solve for w. Subtract 9 from both sides.
5w+=+-9 Now divide both sides by 5 to isolate the variable.
w+=+%28-9%29%2F5
So when w = %28-9%29%2F5, the given expression becomes...
4%2F%285%28-9%2F5%29%2B9%29+=+4%2F%28-9%2B9%29=4%2F0 Undefined!