Question

Simplify:
$\frac{ {a}^{2} + ab }{a - b} \div \frac{ab}{ {a}^{2} - {b}^{2} }$
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Answer 1

9514 1404 393

Answer:

  (a+b)²/b

Step-by-step explanation:

Invert the denominator fraction and multiply.

  $\dfrac{a^2+ab}{a-b}\div\dfrac{ab}{a^2-b^2}=\dfrac{a(a+b)}{a-b}\cdot\dfrac{a^2-b^2}{ab}\\\\=\dfrac{a(a+b)(a+b)(a-b)}{ab(a-b)}=\boxed{\dfrac{(a+b)^2}{b}}$