Step-by-step explanation:
[tex] \dfrac{a}{b+1} - \dfrac{a}{(b+1)^2} = [/tex]
[tex] = \dfrac{b + 1}{b + 1} \times \dfrac{a}{b+1} - \dfrac{a}{(b+1)^2} [/tex]
[tex] = \dfrac{a(b + 1)}{(b+1)^2} - \dfrac{a}{(b+1)^2} [/tex]
[tex] = \dfrac{ab + a}{(b+1)^2} - \dfrac{a}{(b+1)^2} [/tex]
[tex] = \dfrac{ab + a - a}{(b+1)^2} [/tex]
[tex] = \dfrac{ab}{(b+1)^2} [/tex]
Answer:
Proof
Step-by-step explanation:
[tex] \frac{a}{(b + 1)} - \frac{a}{ {(b + 1)}^{2} } [/tex]
Multiply the first fraction (the numerator and the denominator) by
[tex](b + 1) \\[/tex]
In order to get common denominators for both fractions
[tex] \frac{a(b + 1)}{ {(b + 1)}^{2} } - \frac{a}{ {(b + 1)}^{2} } [/tex]
Then expand the first fraction's numerator and subtract fractions to get your answer
[tex] \frac{ab + a}{ {(b + 1)}^{2} } - \frac{a}{ {(b + 1)}^{2} } = \frac{ab}{ {(b + 1)}^{2} } [/tex]
