Question

Please Help!! Due Tonight!!!

Given the equation 6/x-3 + 5/x+3 = 10/x^2-9.  Part A: What values of x that would make the equation no solution? Why? Part B: What is the solution to the equation. Show all of your steps.

Answer 1

x cannot = 3 or -3; solution is x = 7/11.

Explanation:

I believe you meant 6 / (x-3) + 5 / (x+3) = 10 / (x^2 - 9). Those parentheses are important, to avoid ambiguity.

Part A:

Then: x cannot be 3, as the first term would then be undefined.

Also: x cannot be -3, as then the 2nd term would be undefined.

Multiply all three terms by the LCD, which is (x-3)(x+3):

6(x+3) + 5(x-3) = 10

Performing the indicated multiplication,

6x + 18 + 5x - 15 = 10. Then 11x + 3 = 10, or 11x = 7, or x = 7/11.

This is the solution (Part B).