Question

Simplify quantity 1 over 36 minus 1 over x squared all over 1 over 6 plus 1 over x.

Answer 1

 [ (1 / 36) - (1 / x²) ] / [ (1 / 6) + (1 / x) ] 

[ (x² - 36) / 36x² ] / [ (x + 6) / 6x ] 

remember that: 
x² - 36 = (x + 6)(x - 6) 

so

[ (x+6)(x-6) / 36x² ] / [ (x + 6) / 6x ] 


[ (x+6)(x-6) / 36x² ] * [ 6x / (x + 6) ] 


6x / 36x² = 1 / 6x 


[ (x+6)(x-6) / 6x ] * [ 1 / (x+6) ] -------------------- > (x - 6) / 6x

The answer is (x - 6) / 6x