Answer:
u² - v²
Step-by-step explanation:
[tex] \dfrac{u^2 - v^2}{u + v} \div \dfrac{u}{u^2 + vu} = [/tex]
[tex] = \dfrac{u^2 - v^2}{u + v} \times \dfrac{u(u + v)}{u} [/tex]
[tex] = \dfrac{(u^2 - v^2)(u)(u + v)}{u(u + v)} [/tex]
[tex] = u^2 - v^2 [/tex]
