Unit 5: Algebraic Fractions — Exercise 5 3

5.3.1.(i) Simplify: 24lm/(5l+10m) * (5l^2 - 20m^2)/(16mn) (ii) Simplify: (x^2-3x+2)/(x^2+3x-4) * (2x^2+8x)/(3x+6) (iii) Simplify: (a^2-4b^2)/(a^2+2ba) * (2a^2+10ab)/(a^2+3ab-10b^2) (iv) Simplify: [(a+b)^2-c^2]/[(a+c)^2-b^2] * [a^2-(b-c)^2]/[(a+c)^2-c^2] (v) Simplify: (x^3-8)/(x^2-4) ÷ (x^2+2x+4)/(x^2+4x+4) (vi) Simplify: (a^2+ab)^2/(a^2-ab)^2 ÷ [(a+b)/(a-b)]^2 (vii) Simplify: (x^2-x-6)/(x^2-x-20) ÷ {(x^3-3x^2)/(x^2+4x) * (x^3-5x^2-14x)/(x^2-12x+35)} (viii) Simplify: (3x^2-3xy)/(10x^2+10xy-20y^2) * (5xy+10y^2)/(6x^2+6xy+6y^2) ÷ (2x^2-2y^2)/(4x^3-4y^3) (ix) Simplify: (2x^2-98)/(x^3-125) * (x^2-3x-10)/(3x-21) ÷ (x^2+5x-14)/(x^2+5x+25) (x) Simplify: (x^2-2x)/(2x+6) * (x^2+x-6)/(x^2-5x) * (6x-30)/(x^2-2x)