OPERATIONS WITH RATIONAL EXPRESSIONS WORKSHEET

(1)  Simplify

(i)  (4x² y / 2z²) ⋅ (6xz³/20y⁴)    Solution

(ii)  (p² - 10p + 21)/(p - 7)⋅ (p² + p - 12)/(p-3)²     Solution

(iii)  [5t³/(4t - 8)] ⋅ [(6t - 12)/10t]     Solution

(2)  Simplify 

(i) [(x + 4)/(3x + 4y)] ⋅ [(9x² - 16y²)/(2x² + 3x - 20)]

Solution

(ii) [(x³ - y³)/(3x²+9xy+6y²) ⋅ (x² + 2xy + y²)/(x² - y²)

Solution

(3) Simplify

(i)  [(2a²+5a+3)/(2a²+7a+6)] ÷ [(a²+6a+5)/(-5a²-35a-50)] 

Solution

(ii)  [(b² + 3b - 28)/(b² + 4b + 4)] ÷ [(b² - 49)/(b² - 5b - 14)]      Solution

(iii)  [(x + 2)/4y] ÷ [(x² - x - 6)/12y²]     Solution

(iv)  [(12t² - 22t + 8)/3t] ÷ [(3t² + 2t - 8)/(2t²+4t)]     Solution

(4)  If x = (a² + 3a - 4)/(3a² - 3) and y = (a² + 2a - 8)/(2a² - 2a - 4) find the value of x²y^-2    Solution

(5)  If a polynomial p(x) = x² −5x −14 is divided by another polynomial q(x) we get (x - 7)/(x + 2), find q (x).   Solution

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