Question 102319
Given h(x)=-3(3-x)/x, solve for h(x+a)-h(x).
{{{h(x)=-3(3-x)/x}}} Original equation.
{{{h(x)=(-9+3x)/x}}} Distributive property.
{{{h(x)=-9/x+3}}}Simplify. 
{{{h(x)=3-9/x}}} Simplified expression. 
{{{h(x+a)=3-9/(x+a)}}} Plug in (x+a)
{{{h(x+a)-h(x)=3-9/(x+a)-(3-9/x)}}}
{{{h(x+a)-h(x)=3-9/(x+a)-3+9/x)}}}
{{{h(x+a)-h(x)=9/x-9/(x+a))}}}
{{{h(x+a)-h(x)=(x(x+a))/(x(x+a))*(9/x-9/(x+a)))}}} Multiply top and bottom of RHS by x(x+a).
{{{h(x+a)-h(x)=(9(x+a)-9x)/(x(x+a)))}}} Multiply top and bottom of RHS by x(x+a).
{{{h(x+a)-h(x)=(cross(9x)+9a-cross(9x))/(x(x+a)))}}} Distribute and simplify.
{{{h(x+a)-h(x)=(9a)/(x(x+a)))}}} Distribute and simplify.