SOLUTION: What is the solution set of the equation (x/x-4)-(1/x+3)=(28/x^2-x-12)? Please help and thank you! I really appreciate it.

Algebra ->  Test -> SOLUTION: What is the solution set of the equation (x/x-4)-(1/x+3)=(28/x^2-x-12)? Please help and thank you! I really appreciate it.       Log On


   

Question 696652: What is the solution set of the equation (x/x-4)-(1/x+3)=(28/x^2-x-12)?
Please help and thank you! I really appreciate it.
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

What is the solution set of the equation (x/x-4)-(1/x+3)=(28/x^2-x-12)?
Please help and thank you! I really appreciate it.

x%2F%28x+-+4%29+-+1%2F%28x+%2B+3%29+=+28%2F%28x%5E2+-+x+-+12%29

** Note that for this equation, x+%3C%3E+4, and x+%3C%3E+-+3

x(x + 3) - 1(x - 4) = 28 ----- Multiplying by LCD, (x - 4)(x + 3), or x%5E2+-+x+-+12

x%5E2+%2B+3x+-+x+%2B+4+=+28

x%5E2+%2B+2x+%2B+4+-+28+=+0%29%29%29%0D%0A%0D%0A%0D%0A%7B%7B%7Bx%5E2+%2B+2x+-+24+=+0

(x + 6)(x - 4) = 0

x + 6 = 0 ----- highlight%28x+=+-+6%29

x - 4 = 0 ---- highlight%28x+=+4%29. However, as stated previously, x+%3C%3E+4.

Therefore, only solution is: highlight_green%28x+=+-+6%29

You can do the check!!

Send comments and “thank-yous” to “D” at MathMadEzy@aol.com