SOLUTION: Solve the equation 1/x+3 - 1/x+4 = 1/2. The solutions are x1= ____ and x2= ____

Algebra ->  Equations -> SOLUTION: Solve the equation 1/x+3 - 1/x+4 = 1/2. The solutions are x1= ____ and x2= ____      Log On


   

Question 346721: Solve the equation 1/x+3 - 1/x+4 = 1/2. The solutions are x1= ____ and x2= ____
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28x%2B3%29+-+1%2F%28x%2B4%29+=+1%2F2
Use the common denominator, %28x%2B3%29%2A%28x%2B4%29


Multiply both sides by 2.
%282%28x%2B4%29-2%28x%2B3%29-%28x%2B3%29%28x%2B4%29%29%2F%28%28x%2B3%29%28x%2B4%29%29=0
%282x%2B8-2x-6-%28x%5E2%2B7x%2B12%29%29%2F%28%28x%2B3%29%28x%2B4%29%29=0
%282-x%5E2-7x-12%29%2F%28%28x%2B3%29%28x%2B4%29%29=0
-%28x%5E2%2B7x%2B10%29%2F%28%28x%2B3%29%28x%2B4%29%29=0
%28%28x%2B2%29%28x%2B5%29%29%2F%28%28x%2B3%29%28x%2B4%29%29=0
Two solutions:
x%2B2=0
highlight%28x=-2%29
.
.
.
x%2B5=0
highlight%28x=-5%29
.
.
.