quotient and simplify

Question

35m²+32mn-12n/15m²-2mn-24n²  divde by 35m²+11mn-6n²/35m²+61mn+24n²  Find the quotient and simplify

Answer 1

Hi Caroline,

 

Correct me if I am wrong, but I think your problem is

 

(35m² + 32mn -12n²)/(15m² - 2mn - 24n²) ÷ (35m² + 11mn -6n²)/(35m² + 61mn + 24n²)

 

= (35m² + 32mn -12n²)/(15m² - 2mn - 24n²) • (35m² + 61mn + 24n²)/(35m² + 11mn -6n²) where the problem becomes a multiplication problem where we invert the second rational expression.

 

= ((7m - 2n)(5m + 6n))/((5m + 6n)(3m - 4n)) • ((7m + 8n)(5m + 3n))/((7m - 2n)(5m + 3n))

 

The factors (7m - 2n), (5m + 6n), and (5m + 3n) cancel, leaving the final simplified rational expression:

 

(7m + 8n)/(3m - 4n))