text: # Simplify: `(2a^2 - 12a + 18)/(3a^2 - 12)` `xx`  `(a^2 + a - 6)/(4a^2 - 36)` Keep (  ) around binomial factors.  Leave answer in factored form.
  
  lemjay | High School Teacher | (Level 2) Senior Educator
  
  Posted on
  
  `(2a^2-12a+18)/(3a^2-12)xx(a^2+a-6)/(4a^2-36)`
  
  To simplify,  factor the polynomials.
  
  `=(2(a^2-6a+9))/(3(a^2-4))xx(a^2+a-6)/(4(a^2-9))`
  
  `=(2(a-3)(a-3))/(3(a+2)(a-2))xx((a+3)(a-2))/(4(a-3)(a+3))`
  
  Then, cancel the common factors between numerators and denominators.
  
  `=(a-3)/(3(a+2))xx1/(2(a+3))`
  
  `=(a-3)/(6(a+2))`
  
  Hence, `(2a^2-12a+18)/(3a^2-12)xx(a^2+a-6)/(4a^2-36)=(a-3)/(6(a+2))` .
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