Help on math pls

Question

Kristen and Christina disagreed with where the graph of k(x)=10x/x^2-x-6 and c(x)=x/x-3 + 4/x+2 intersect. Kristen  believes that the grass can only intersect at 6. Christina believes that the graphs can intersect at both -2 and 6. 

 

Which of the following statements are true? 

 

A. Kristen is correct because -2 would make one of the fractions be undefined

 

B.  Christina is correct because these are the solutions to the functions when they are equal to each other.

 

C.  Neither of them are correct because -2 and six are not solutions to the above systems and functions. 

 

D.  There is no way of telling  

Answer 1

Consider the function k(x). Is the function defined for all x? No, the function is undefined where the denominator equals 0 because division by 0 is undefined. Set x² - x- 6 = 0 and solve for x. Once you do, you should be able to eliminate at least one of the choices in the above multiple choice list.

 

You can also set k(x) = c(x) to see whether there are any real numbers x that are a solution to the problem.

 

10x/(x² - x - 6) = x/(x - 3) + 4/(x + 2)

 

To solve this, find the LCD, which you should be able to determine is (x + 2)(x - 3).

 

Let me know if you encounter any difficulties.