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
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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) (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:
(y + 5)}+\frac{y}{(y + 2)(y - 2)} = \frac{y}{(y - 2)(y + 5)})
Three different factors in all the denominators, so the LCD is:
(y - 2)(y + 5))
Apply the LCD:
 + y(y + 5)}{(y + 2)(y - 2)(y + 5)} = \frac{y(y + 2)}{(y + 2)(y - 2)(y + 5)})
Multiply both sides by the LCD to eliminate the denominators:
 + y(y + 5) = y(y + 2))
Distribute to remove parentheses:
Collect like terms on the left:
Factor:
 = 0)
Use the Zero Product Rule:
or
Verification of all elements of the solution set is left as an exercise for the student.
John
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