Simplify using the order of operations

-32 + 3[12 ÷ (5 - 8)]
= -32 + 3[12 ÷ (-3)] {subtracted 5 - 8}
= -32 + 3(-4) {divided 12 by -3}
= -32 - 12 {multiplied 3 by -4}
= - 44 {subtracted}

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Simplify the rational expression

-x² + 10x - 21
-----------------
-3x² + 23x - 14 


-1(x² - 10x + 21)
---------------------- {factored -1 out of top and bottom}
-1(3x² - 23x + 14) 


(x - 7)(x - 3)
---------------- {cancelled the -1's and factored into 2 binomials}
(3x - 2)(x - 7) 


  x - 3
---------- {cancelled x - 7 on top and bottom}
 3x - 2 

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Simplify the rational expression

28x² - 29x + 6
--------------------
-28x² + 50x - 12 


   (7x - 2)(4x - 3)
----------------------- {factored -2 out, & bottom into two binomials}
-2(14x² - 25x + 6) 


 (7x - 2)(4x - 3)
---------------------- {factored bottom into two binomials}
-2(7x - 2)(2x - 3) 


   4x - 3
------------ {cancelled 7x - 2 on top and bottom}
-2(2x - 3) 

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