Question

Сократите пример/Спростіть вираз

Answer 1

$4$

Объяснение:

$\bigg (\dfrac{3}{y-4}+\dfrac{2y}{y+1}+\dfrac{4y-6}{y^{2}-3y-4} \bigg ) \cdot \dfrac{4y-16}{2y-3}=\bigg (\dfrac{3}{y-4}+\dfrac{2y}{y+1}+\dfrac{4y-6}{y^{2}-4y+y-4} \bigg ) \cdot$

$\cdot \dfrac{4y-16}{2y-3}=\bigg (\dfrac{3}{y-4}+\dfrac{2y}{y+1}+\dfrac{4y-6}{y(y-4)+1(y-4)} \bigg ) \cdot \dfrac{4y-16}{2y-3}=$

$= \bigg (\dfrac{3}{y-4}+\dfrac{2y}{y+1}+\dfrac{4y-6}{(y-4)(y+1)} \bigg ) \cdot \dfrac{4y-16}{2y-3}=\dfrac{3(y+1)+2y(y-4)+4y-6}{(y-4)(y+1)} \cdot$

$\cdot \dfrac{4(y-4)}{2y-3}=\dfrac{3y+3+2y^{2}-8y+4y-6}{(y-4)(y+1)} \cdot \dfrac{4(y-4)}{2y-3}=\dfrac{2y^{2}-y-3}{(y-4)(y+1)} \cdot \dfrac{4(y-4)}{2y-3}=$

$=\dfrac{4(2y^{2}-y-3)(y-4)}{(y-4)(y+1)(2y-3)}=\dfrac{4(2y^{2}-y-3)}{2y^{2}-3y+2y-3}=\dfrac{4(2y^{2}-y-3)}{2y^{2}-y-3}=4;$