How do you simplify #((1/(3+h)) - (1/3)) / h#?

1 Answer
Jan 18, 2017

Answer:

Multiply by 1 in the form of #(3(3 + h))/(3(3 + h))#
A common factor of #h/h# will cancel

Explanation:

Given: #(1/(3 + h) - 1/3)/h#

Multiply by 1 in the form of #(3(3 + h))/(3(3 + h))#

#(1/(3 + h) - 1/3)/h(3(3 + h))/(3(3 + h))#

Using the distributive property on the numerators and just multiplication on the denominator:

#((3(3 + h))/(3 + h) - (3(3 + h))/3)/(3h(3 + h))#

Please observe what cancels:

#((3cancel((3 + h)))/cancel((3 + h)) - (cancel3(3 + h))/cancel3)/(3h(3 + h))#

#(3 - (3 + h))/(3h(3 + h))#

Distribute the minus:

#(3 - 3 - h)/(3h(3 + h))#

#(-h)/(3h(3 + h))#

#h/h# cancels:

#(-1)/(3(3 + h))#

#(-1)/(9 + 3h)#