REDUCING RATIONAL EXPRESSIONS TO LOWEST TERMS

Reduce each of the following rational expressions to its lowest term.

Question 1 :

(x² - 1) / (x² + x)

Solution :

  =  (x² - 1) / (x² + x)  

x² - 1  =  (x + 1) (x - 1)

(x² + x)  = x(x + 1)

  =  (x + 1) (x - 1) / x(x + 1)

  =  (x - 1)/x

Question 2 :

(x² - 11x + 18) / (x² - 4x + 4)

Solution :

  =   (x² - 11x + 18)/(x² - 4x + 4)

(x² - 11x + 18)  =  (x - 9)(x - 2)

(x² - 4x + 4)  =  (x - 2)(x - 2)

  =   (x - 9)(x - 2)/(x - 2)(x - 2)

  =  (x - 9)/(x - 2)

Question 3 :

(9x² + 81x) / (x³ + 8x² - 9x)

Solution :

  =   (9x² + 81x) / (x³ + 8x² - 9x)

(9x² + 81x)  =  9x(x + 9)

(x³ + 8x² - 9x)  =  x(x² + 8x - 9)

  =  x(x + 9)(x - 1)

  =   9x(x + 9) / x(x + 9)(x - 1)

  =  9/(x - 1)

Question 4 :

 (p² - 3p - 40) / (2p³-24p²+64p)

Solution :

  =  (p² - 3p - 40)/(2p³ - 24p² + 64p)

p² - 3p - 40  =  (p - 8)(p + 5)

2p³ - 24p² + 64p  =  2p(p² - 12p + 32)

  =  2p (p -8) (p - 4)

  =  (p - 8)(p + 5)/2p (p -8) (p - 4)

  =  (p + 5)/2p (p - 4)

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