**Operations with Rational Expressions Worksheet :**

Here we are going to see some practice questions based on multiplying and dividing rational expressions.

**Multiplication of rational numbers :**

The product of two rational expression is the product of their numerators divided by the product of their denominators and the resulting expression is then reduced to its lowest form.

**Division of rational numbers :**

Thus division of one rational expression by other is equivalent to the product of first and reciprocal of the second expression. If the resulting expression is not in its lowest form then reduce to its lowest form.

(1) Simplify

(i) (4x^{2} y / 2z^{2}) ⋅ (6xz^{3}/20y^{4}) Solution

(ii) (p^{2} - 10p + 21)/(p - 7)⋅ (p^{2} + p - 12)/(p-3)^{2} Solution

(iii) [5t^{3}/(4t - 8)] ⋅ [(6t - 12)/10t] Solution

(2) Simplify

(i) [(x + 4)/(3x + 4y)] ⋅ [(9x^{2} - 16y^{2})/(2x^{2} + 3x - 20)]

(ii) [(x^{3} - y^{3})/(3x^{2}+9xy+6y^{2}) **⋅ (x ^{2} + 2xy + y^{2})/(x^{2} - y^{2})**

**(3) S**implify

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

(ii) [(b^{2} + 3b - 28)/(b^{2} + 4b + 4)] ÷ [(b^{2} - 49)/(b^{2} - 5b - 14)] Solution

(iii) [(x + 2)/4y] ÷ [(x^{2} - x - 6)/12y^{2}] Solution

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

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

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

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