Question

Multiply r^2+7r+10/3 by 3 r-30/r^2-5r-50

Answer 1

r² + 7 r + 10 = r² + 2 r + 5 r + 10 = r ( r + 2 ) + 5 ( r + 2 ) = ( r + 2 ) ( r + 5 )
r² - 5 r - 50 = r² - 10 r + 5 r - 50 = r ( r - 10 ) + 5 ( r - 10 ) = ( r - 10 ) ( r + 5 )

`(r^(2) +7r+10)/(3)* (3r-30)/(r ^(2)-5r-50 )= \\ ((r+5)(r+2))/(3)* (3(r-10))/((r-10)(r+5))` = ( after cancellation ) = r + 2