SOLUTION: The directions say for the pair of functions f and g, find all values of a for which f(a) =g(a) f(x) = y/y^2+7y+10 + y/y^2-4 g(x) = y/y^2+3y-10 my answer was y^2=0 an

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: The directions say for the pair of functions f and g, find all values of a for which f(a) =g(a) f(x) = y/y^2+7y+10 + y/y^2-4 g(x) = y/y^2+3y-10 my answer was y^2=0 an      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 195474: The directions say for the pair of functions f and g, find all values of a for which f(a) =g(a)
f(x) = y/y^2+7y+10 + y/y^2-4
g(x) = y/y^2+3y-10

my answer was y^2=0 and y=0 but I don't think that correct
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Missed it by that much.

Simply set the two functions equal to each other and solve the resulting quadratic:



Factor all three denominators:



Three different factors in all the denominators, so the LCD is:



Apply the LCD:



Multiply both sides by the LCD to eliminate the denominators:



Distribute to remove parentheses:



Collect like terms on the left:



Factor:



Use the Zero Product Rule:

or



Verification of all elements of the solution set is left as an exercise for the student.

John