SOLUTION: x+4/x+2=7/x+2 + 24/x^2-4 Find all the real solutions

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: x+4/x+2=7/x+2 + 24/x^2-4 Find all the real solutions      Log On


   

Question 342387: x+4/x+2=7/x+2 + 24/x^2-4
Find all the real solutions
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First simpify,
%28x%2B4%29%2F%28x%2B2%29=7%2F%28x%2B2%29+%2B+24%2F%28x%5E2-4%29
%28x%2B4-7%29%2F%28x%2B2%29-24%2F%28x%5E2-4%29=0
%28x-3%29%2F%28x%2B2%29-24%2F%28x%5E2-4%29=0
Use the common denominator, x%5E2-4=%28x-2%29%28x%2B2%29

%28x%5E2-2x-3x%2B6-24%29%2F%28%28x-2%29%28x%2B2%29%29=0
%28x%5E2-5x-18%29%2F%28%28x-2%29%28x%2B2%29%29=0
Find the zeros of the numerator using the quadratic formula,
x+=+%285+%2B-+sqrt%28+%285%29%5E2-4%2A1%2A%28-18%29+%29%29%2F%282%2A1%29+
x+=+%285+%2B-+sqrt%28+25%2B72%29%29%2F2+
highlight%28x+=+%285+%2B-+sqrt%28+79%29%29%2F2%29+