Find the quotient and simplify 35m2 57mn 18n235m2 43 mn

Find the quotient and simplify. 35m^2 - 57mn + 18n^2/35m^2 - 43 mn + 12n^2 + 35 m^2 + 12mn - 36n/49m^2 + 98mn + 48n^2 A) (5m + 4n)/(7m - 8n) B) (5m - 6n)^2/(7m + 8n)(5m - 4n C) 7m + 8n/5m - 4n D) (5m + 6n)^2/(7m - 8n)(5m + 4n)

Solution

18.   [(35m² -57mn +18n²)/ (35m² -43mn +12n²)]/ [(35m² -12mn -36n²)/( 49m² +98mn +48n²)] =

          [(35m² -57mn +18n²)/ (35m² -43mn +12n²)]*[ (49m² +98mn +48n²)/ (35m² -12mn -36n²)] =

         Now, 35m² -57mn +18n²= 35m² - 42mn-15mn +18n²= 7m(5m-6n)-3n(5m-6n)= (7m-3n)(5m-6n).

         Also, 35m² -43mn +12n²= 35m² -28mn-15mn +12n²= 7m(5m-4n)-3n(5m-4n) = (7m-3n)(5m-4n).

        49m² +98mn +48n² = 49m² +56mn+42mn +48n² = 7m(7m+8n)+6n(7m+8n)= (7m+6n)(7m+8n), and

        35m² -12mn -36n² =35m² -42mn+30mn -36n²= 7m(5m-6n)+6n(5m-6n) = (7m+6n)(5m-6n). Hence    

        the given expression is[(7m-3n)(5m-6n)/ (7m-3n)(5m-4n)]*[ (7m+6n)(7m+8n)/ (7m+6n)(5m-6n)] =

        (7m+8n)/(5m-4n).

     Option nC is the correct answer.