Question 243609
{{{(12/(x+h+15)-12/(x+15))/h}}} Start with the given expression.



{{{((12(x+15))/((x+15)(x+h+15))-12/(x+15))/h}}} Multiply the first upper fraction by {{{(x+15)/(x+15)}}} to get that denominator equal to the LCD.



{{{((12(x+15))/((x+15)(x+h+15))-(12(x+h+15))/((x+15)(x+h+15)))/h}}} Multiply the second upper fraction by {{{(x+h+15)/(x+h+15)}}} to get that denominator equal to the LCD.
 


{{{((12(x+15)-(12(x+h+15)))/((x+15)(x+h+15)))/h}}} Combine the upper fractions.



{{{(12x+180-12x-12h-180)/((x+15)(x+h+15)))/h}}} Distribute



{{{(-12h)/((x+15)(x+h+15)))/h}}} Combine like terms.



{{{((-12h)/((x+15)(x+h+15)))(1/h)}}} Multiply the upper fraction by the reciprocal of the lower fraction.



{{{((-12*highlight(h))/((x+15)(x+h+15)))(1/highlight(h))}}} Highlight the common terms.



{{{((-12*cross(h))/((x+15)(x+h+15)))(1/cross(h))}}} Cancel out the common terms.




{{{-12/((x+15)(x+h+15))}}} Simplify.



So {{{(12/(x+h+15)-12/(x+15))/h=-12/((x+15)(x+h+15))}}}