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

1 Answer
Jan 18, 2017

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)