Question

Show that a/(b+1) - a/(b+1)^2 can be written as ab/(b+1)^2

Answer 1

Proof

Explanation:

`(a)/((b + 1)) - \frac{a}{ {(b + 1)}^(2) }`

Multiply the first fraction (the numerator and the denominator) by

`(b + 1) \\`

In order to get common denominators for both fractions

`\frac{a(b + 1)}{ {(b + 1)}^(2) } - \frac{a}{ {(b + 1)}^(2) }`

Then expand the first fraction's numerator and subtract fractions to get your answer

`\frac{ab + a}{ {(b + 1)}^(2) } - \frac{a}{ {(b + 1)}^(2) } = \frac{ab}{ {(b + 1)}^(2) }`

Answer 2

Explanation:

`(a)/(b+1) - (a)/((b+1)^2) =`

`= (b + 1)/(b + 1) * (a)/(b+1) - (a)/((b+1)^2)`

`= (a(b + 1))/((b+1)^2) - (a)/((b+1)^2)`

`= (ab + a)/((b+1)^2) - (a)/((b+1)^2)`

`= (ab + a - a)/((b+1)^2)`

`= (ab)/((b+1)^2)`