SOLUTION: This question is on Rational Expressions, and solving them using the Algebraic method to find the vertical asymptote. g(x)=(x^2+x+1)/(5x^2+1) I can't figure out where to start.

Question 185346: This question is on Rational Expressions, and solving them using the Algebraic method to find the vertical asymptote.
g(x)=(x^2+x+1)/(5x^2+1) I can't figure out where to start...
Also simplifying (3a^2-6a)/(12-6a) What the heck is this? And where do I start and finish this crazy problem???
Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
Vertical asymptotes occur as the value of denominator approaches 0 (which causes the quotient to approach infinity).
So find the values that make the denominator 0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -20 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -20 is + or - .

The solution is

Here's your graph:

no real values of x cause that to happen, so the answer is 'there are no vertical asymtotes' for this expression.
See this URL for more info --> http://www.purplemath.com/modules/asymtote.htm
Simplify

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

Start with the given function.

Set the denominator equal to zero. Remember, vertical asymptotes arise only when there's a division by zero

Subtract 1 from both sides.

Divide both sides by 5

Take the square root of both sides.

Remember, you CANNOT take the square root of a negative number. So this means that the value of "x" will be complex/imaginary.

In other words, there is NO value of "x" that will make the denominator zero.

So there are no vertical asymptotes (graph the function to verify)

===============================================================

# 2

Start with the given expression

Factor the numerator

Factor the denominator

Reduce (the outer coefficients) to get

Highlight the common terms.

Cancel out the common terms.

Simplify

==============

Answer:

So simplifies to

In other words, where
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