how to solve 7y^2-42y/y^2-3y-54 divided by y-6/y+6

Question

the first equation is top over bottom divided by top over bottom i know you have to flip the second equation but how do you solve

Answer 1

7y^2-42y        7y(y - 6)

------------  =  -------------    

y^2-3y-54      (y - 9)(y + 6)

                       ----------------

                        (y - 6)

                       ----------

                        (y + 6)

to divide fraction you multiply by the reciprical (turn the bottom fraction upside down

7y(y - 6)                  (y + 6)           7y

-------------       *         ---------  =    ---------

(y - 9)(y + 6)              (y - 6)            (y - 9)