How many real-number solutions does the equation have?
2 answers:
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The question is asking us to divide the function f(x) by the function g(x).
Knowing this, we can perform the division:
(2x+1)/(x^2-7) = (f/g)(x)
The simplest answer is
, as there is no way to further simplify the problem. This means that there is a discontinuity where 
, as it is impossible to divide by 0.
Knowing this, we can perform the division:
(2x+1)/(x^2-7) = (f/g)(x)
The simplest answer is
Answer:
B
Step-by-step explanation:
+ 6 = x ( subtract 6 from both sides )
= x - 6 ( square both sides )
x = (x - 6)² ← expand using FOIL
x = x² - 12x + 36 ( subtract x from both sides )
0 = x² - 13x + 36 , that is
x² - 13x + 36 = 0 ← in standard form
(x - 4)(x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x - 9 = 0 ⇒ x = 9
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
x = 4
left side = + 6 = 2 + 6 = 8
right side = x = 4
Since 8 ≠ 4 then x = 4 is an extraneous solution
x = 9
left side = + 6 = 3 + 6 = 9
right side = x = 9
Thus the solution is x = 9 → B