Subtract and Simplify

Question

((x+3)/(x²-3x-28)) - ((2)/(x²-49))

Answer 1

First, factor all terms where possible.

 

[(x + 3) / (x - 7)(x + 4)] / [2 / (x - 7)(x + 7)]

 

 

Then, look for the LCD.  The LCD is (x - 7)(x + 7)(x + 4).

 

Multiply the top and bottom of first rational expression by (x + 7).

Multiply the top and bottom of second rational expression by (x + 4).

 

Subtract the numerators.  Then simplify as needed.