# 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

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

(2)  Simplify

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

(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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