Question

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

Answer 1

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)`