Rational Expressions - Add/Subtract - Part 2

(x2 - 5x + 4) / (x2 - 2x - 8)      -      (x2 - 9) / (x2 + 5x + 6)

(x - 1)(x - 4) / (x + 2)(x - 4)      -      (x - 3)(x + 3) / (x + 2)(x + 3)

(x - 1)/ (x + 2)      -      (x - 3) / (x + 2)

[ (x - 1) - (x - 3) ]    /    (x + 2)

[ x - 1 - x + 3 ]    /    (x + 2)

x     /     (x + 2)

Given

Factored each polynomial

Canceled out the factors (x - 4) on the left and (x + 3) on the right

Combined fractions

Distributed the negative in front of the parenthesis

Combined like terms

(x2 + 5x) / (2x2 + 6x - 20)      +      (x2 - 1) / (x2 - 3x + 2)

x(x + 5) / [ 2(x - 2)(x + 5) ]      +      (x - 1)(x + 1) / (x - 1)(x -2)

x / [ 2(x - 2) ]     +      (x + 1) / (x - 2)

x / [ 2(x - 2) ]     +      (x + 1) / (x - 2)    *   2/2

x / [ 2(x - 2) ]     +      2(x + 1) / [ 2(x - 2) ]

{ x + 2(x + 1) }      /      [ 2(x - 2) ]

{ x + 2x + 2) }      /      [ 2(x - 2) ]

{ 3x + 2 }      /      [ 2(x - 2) ] 

Given

Factored each polynomial

Canceled out the factors (x + 5) on the left and (x - 1) on the right

Multiplied the fraction on the right by 2/2

Smashed the numbers together to get of multiplication sign

Combined fractions

Distributed the negative in front of the parenthesis

Combined like terms