SOLUTION: Find the vertical asymptotes of F(x)= (3x+5)/(6x^2-x-2). Would this problem be x=1/2, x=-2/3. or x-1/2, x 2/3 I am not sure about this one. Any help would be greatly appreci

Algebra ->  Rational-functions -> SOLUTION: Find the vertical asymptotes of F(x)= (3x+5)/(6x^2-x-2). Would this problem be x=1/2, x=-2/3. or x-1/2, x 2/3 I am not sure about this one. Any help would be greatly appreci      Log On


   

Question 207647This question is from textbook
: Find the vertical asymptotes of F(x)= (3x+5)/(6x^2-x-2).
Would this problem be x=1/2, x=-2/3. or x-1/2, x 2/3
I am not sure about this one. Any help would be greatly appreciated. Thank you for your time and for your help.
 This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the vertical asymptotes, simply set the denominator equal to zero to get 6x%5E2-x-2=0. From there, solve for 'x' to find the x values that make the denominator equal to zero. These x values will be the equations of the vertical asymptotes.








If you don't know how to solve, then....



6x%5E2-x-2=0 Start with the given equation.


Notice that the quadratic 6x%5E2-x-2 is in the form of Ax%5E2%2BBx%2BC where A=6, B=-1, and C=-2


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%286%29%28-2%29+%29%29%2F%282%286%29%29 Plug in A=6, B=-1, and C=-2


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%286%29%28-2%29+%29%29%2F%282%286%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%286%29%28-2%29+%29%29%2F%282%286%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--48+%29%29%2F%282%286%29%29 Multiply 4%286%29%28-2%29 to get -48


x+=+%281+%2B-+sqrt%28+1%2B48+%29%29%2F%282%286%29%29 Rewrite sqrt%281--48%29 as sqrt%281%2B48%29


x+=+%281+%2B-+sqrt%28+49+%29%29%2F%282%286%29%29 Add 1 to 48 to get 49


x+=+%281+%2B-+sqrt%28+49+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%281+%2B-+7%29%2F%2812%29 Take the square root of 49 to get 7.


x+=+%281+%2B+7%29%2F%2812%29 or x+=+%281+-+7%29%2F%2812%29 Break up the expression.


x+=+%288%29%2F%2812%29 or x+=++%28-6%29%2F%2812%29 Combine like terms.


x+=+2%2F3 or x+=+-1%2F2 Simplify.


So the solutions are x+=+2%2F3 or x+=+-1%2F2



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Answer:


This means that the vertical asymptotes of f%28x%29=%283x%2B5%29%2F%286x%5E2-x-2%29 are x+=+2%2F3 and x+=+-1%2F2