Solve the equation. Check all proposed solutions. Show work in solving and in checking.

Question

Solve the equation. Check all proposed solutions. Show work in solving and in checking.

 

   x      +    x     =  102 

 x-3         x+3      x^2-9

 

Answer 1

Solve the equation. Check all proposed solutions. Show work in solving and in checking.

  x         x       102

----  +  ---- =  -----       
x-3      x+3     x²-9

 

First let's add the fractions on the left.  To add any fraction, you must put them over a common denominator, in this case (x-3)(x+3)

 

   x   (x+3)          x   (x-3)

------ ------  +  ------ -------

(x-3) (x+3)      (x+3) (x-3)

 

Multiply out the numerator and denominator then combine like terms

 

x² + 3x + x² - 3x          2x²
---------------------  =   ------  
       x² - 9                  x²-9

 

Now we can re-state the original problem as:

 

2x²/(x²-9) = 102/(x²-9)

 

2x² = 102      (Multiply both sides by (x²-9) )

 

x² = 51         (Divide both sides by 2)

 

x = ±√51      (Take the square root of both sides)

 

To check, plug x = +√51 and x = -√51 into your original equation (below) and make sure the left hand side equals the right hand side.  If it does, it's a solution.

 

 2x²/(x²-9) = 102/(x²-9)