Simplify Rational expressions

Question

Simplify

 

1/x+h  - 1/x

        H

Answer 1

Numerator = 1/(x+h) - 1/x

Denominator = H 

 

Put the terms in the numerator over their common denominator x*(x+h)   

 

Numerator = x/[x*(x+h)] - (x+h)/[x*(x+h))] = (x - x - h) / [x^2 + x*h]  = -h/(x^2 + x*h) 

 

Dividing this expression by H is the same as multiplying by (1/H) to get 

 

-h/(H*[x^2+x*h)] = -h/[H*x^2 + H*x*h] 

 

If little h and big H are different variables this is it.  But if they are the same variable they will cancel to leave 

 

-1/(x^2 + h*x)