Using the PEDMAS order of operation, first execute the Multiplication operations:
color(red)(9)/color(red)(4) xx color(red)(2)/color(red)(3) + color(blue)(4)/color(blue)(5) xx color(blue)(5)/color(blue)(3) =>94×23+45×53⇒
(color(red)(9) xx color(red)(2))/(color(red)(4) xx color(red)(3)) + (color(blue)(4) xx color(blue)(5))/(color(blue)(5) xx color(blue)(3)) =>9×24×3+4×55×3⇒
18/12 + 20/15 =>1812+2015⇒
(6 xx 3)/(6 xx 2) + (5 xx 4)/(5 xx 3) =>6×36×2+5×45×3⇒
(color(red)(cancel(color(black)(6))) xx 3)/(color(red)(cancel(color(black)(6))) xx 2) + (color(blue)(cancel(color(black)(5))) xx 4)/(color(blue)(cancel(color(black)(5))) xx 3) =>
3/2 + 4/3
Now, after putting each fraction over a common denominator we can add the fractions:
(3/3 xx 3/2) + (2/2 xx 4/3) =>
(3 xx 3)/(3 xx 2) + (2 xx 4)/(2 xx 3) =>
9/6 + 8/6 =>
(9 + 8)/6 =>
17/6
