Algebra Honors (Periods 5 & 6)

Dividing Fractions 6-3

Use the same rule for dividing fraction that you use for dividing real numbers—multiply by its reciprocal.    
a/b  ÷ c/d = a/b ∙ d/c

Divide           x/2y  ÷ xy/4   so 

  x/2y  ∙ 4/xy

Simplify to 2/y²       

Divide  18/(x²-25) ÷   [24/(x+5)]

That becomes

18/(x²-25) ∙   [(x+5)/24]

     =  [3 ∙ 6/(x+5)(x-5)] ∙   [(x+5)/4 ∙ 6]

 Simplify

= 3/4(x+5)

Divide:

[x²+3x-10/(2x+6)]    ÷ [(x²-4)/ (x²-x-12)]

Which becomes

[x²+3x-10/(2x+6)]  ∙ [(x²-x-12)/ (x²-4)]

Factor

 [(x+5)(x-2)/2(x+3)]  ∙ [(x+3)(x-4)/ (x+2)(x-2)]

 [(x+5)(x-4)]/[2(x+2)]   

Make sure to use the O³ when simplifying an expression that involves more than one operation.   For Example:

   (2x/y)³÷(y²/x) ∙  x/4

= (8x³/y³⁾∙ (x/y²) ∙  x/4

2x³ /4