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

2 Answers

3 votes

Answer:

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) }

User Musma
by
6.7k points
3 votes

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)

User Tmg
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7.3k points