Question

On the question of =When is the Rational Expression Undefined, How do I solve these problems:
3/x ; 4/2-x; 5/xsquared-25; x-4/xsquared-4x+3; 5/x squared+1
Please give clear, concise directions and explanations
Please do NOT send me youtube tutorials; I have BSOD (BlueScreenOfDeath), and playing videos causes it to happen. Thank you.

Answer 1

You want to find when the bottom part, the denominator, is equal to 0. Since you can not divide by 0, the expression is undefined at those points.

Answer 2

If the denominator is a linear equation, just solve for x. If it is a quadratic equation, use the quadratic formula to find when it is equal to 0.

Answer 3

For example\[\frac{5}{x^2-25} \]Denominator is \(x^2-25\). So we find\[
x^2-25=0
\]In this case we don't even need quadratic formula, since we have a difference of squares and those are easy to factor \[
(x-5)(x+5)=0
\]So this equation is satisfied when \(x=5 \) or \(x=-5\). That means the expresson \(\large \frac{5}{x^2-25}\) is undefined at those values of \(x\).

Answer 4

for the 5th problem I put up :\[\frac{ 5 }{ x ^{2}+1 }\] There is no way to factor for that.

Answer 5

Which means that is is always defined.

Answer 6

You'd need a complex number to get it equal to 0, but for these problems we tend to stick to just real numbers.

Answer 7

Alright, on a different question, I was given a product(-5) and a sum(-4) I have to write the quadratic equation using the formula \[ax^2+bx+c\] How do I know which terms are a b and c, and how do I know where to place them