consider the expression

Question

• simplify this expression: (t³ - 9t) / (t(t+3)³)

 

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Consider the expression (x² - 4) / (x² + 4)

• evaluate the expression for x = 0 and x = 1/2
• find the values of x for which this expression is undefined
• find two values of x for which the numerator of the expression is equal to zero

Answer 1

simplify this expression: (t³ - 9t) / (t(t+3)³)

 

Factor numerator: t(t+3)(t-3)

 

Factor denominator: t(t+3)(t+3)²

 

You see (I hope) that the first two factors of numerator and denominator are identical, so they 'cancel', giving

(t-3)/(t+3)²

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Consider the expression (x² - 4) / (x² + 4)

a) when x = 0, this is equal to -1, by substitution

b) You can do this substitution, x = ½

c) Since the denominator can never be zero, this expression is defined for all Reals

d) This expression is zero if and only if the numerator is zero; x = ±2