Question

simplifique a fração algébrica abaixo (m/m-n-1/2).m²-n²/n

Answer 1

Lembrete:

๏ $a^2-b^2=\left(a+b\right)\cdot \left(a-b\right)$
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$\left(\dfrac{m}{m-n}-\dfrac{1}{2}\right)\cdot \dfrac{m^2-n^2}{n}\\\\\left(\dfrac{2m-\left(m-n\right)}{2\left(m-n\right)}\right)\cdot \dfrac{m^2-n^2}{n}\\\\\left(\dfrac{m+n}{2\left(m-n\right)}\right)\cdot \dfrac{m^2-n^2}{n}\\\\\dfrac{m+n}{2\left(m-n\right)}\cdot \dfrac{\left(m+n\right)\cdot \left(m-n\right)}{n}\\\\\dfrac{m+n}{2}\cdot \dfrac{\left(m+n\right)}{n}\\\\\dfrac{m+n}{2}\cdot \dfrac{m+n}{n}\\\\\boxed{\bold{\frac{\left(m+n\right)^2}{2m}}}$