1) $\frac{3x}{4x^2} \cdot \frac{6x^2}{3} = \frac{18x^3}{12x^2} = \frac{3x}{2}$, excluded values: $x \neq 0$
2) $\frac{2x}{6x^2} \cdot \frac{10}{10x} = \frac{20x}{60x^3} = \frac{1}{3x^2}$, excluded values: $x \neq 0$
3) $\frac{3}{5(3x-8)} \cdot \frac{5(3x-8)}{2} = \frac{15(3x-8)}{10(3x-8)} = \frac{3}{2}$, excluded values: $x \neq \frac{8}{3}$
4) $\frac{(x+10)(x+3)}{x+10} \cdot \frac{(x-3)(x+10)}{x+3} = (x+3)(x-3) = x^2 - 9$, excluded values: $x \neq -10, -3$
5) $\frac{-6a}{9n^2+9n} \cdot \frac{9n^2+9n}{2a} = \frac{-54a(n^2+n)}{18a(n^2+n)} = -3$, excluded values: $a \neq 0, n \neq 0, -1$
6) $\frac{3x^2-24x}{8} \cdot \frac{1}{x-8} = \frac{3x(x-8)}{8(x-8)} = \frac{3x}{8}$, excluded values: $x \neq 8$
7) $\frac{6x+24}{x-9} \cdot \frac{7x^2-63x}{x^2-3x-28} = \frac{6(x+4)}{x-9} \cdot \frac{7x(x-9)}{(x-7)(x+4)} = \frac{42x}{x-7}$, excluded values: $x \neq 9, -4, 7$
8) $\frac{3x^2-3x}{x^2+x-12} \cdot \frac{10x-30}{x-1} = \frac{3x(x-1)}{(x+4)(x-3)} \cdot \frac{10(x-3)}{x-1} = \frac{30x}{x+4}$, excluded values: $x \neq 1, 3, -4$
9) $(x+2) \cdot \frac{x+8}{10x+80} = (x+2) \cdot \frac{x+8}{10(x+8)} = \frac{x+2}{10}$, excluded values: $x \neq -8$
10) $\frac{1}{a-7} \cdot \frac{5a^2+45a}{a+9} = \frac{1}{a-7} \cdot \frac{5a(a+9)}{a+9} = \frac{5a}{a-7}$, excluded values: $a \neq -9, 7$
11) $\frac{8}{4x^2} \cdot \frac{8x^2}{2} = \frac{64x^2}{8x^2} = 8$, excluded values: $x \neq 0$
12) $\frac{9}{3} \cdot \frac{5}{10a} = 3 \cdot \frac{5}{10a} = \frac{15}{10a} = \frac{3}{2a}$, excluded values: $a \neq 0$
13) $\frac{x^2-10x+21}{x-3} \cdot \frac{x^2-10x+21}{x-7} = \frac{(x-7)(x-3)}{x-3} \cdot \frac{(x-7)(x-3)}{x-7} = (x-7)(x-3) = x^2 - 10x + 21$, excluded values: $x \neq 3, 7$
14) $\frac{10}{x+4} \cdot \frac{10x+40}{x^2-2x-24} = \frac{10}{x+4} \cdot \frac{10(x+4)}{(x-6)(x+4)} = \frac{100}{(x-6)(x+4)}$, excluded values: $x \neq -4, 6$
15) $\frac{10x^2(n-4)}{(n-9)(n-4)} \cdot \frac{3}{3(n-9)} = \frac{10x^2}{n-9} \cdot \frac{1}{n-9} = \frac{10x^2}{(n-9)^2}$, excluded values: $n \neq 4, 9$
16) $\frac{p-7}{9(p-7)} \cdot \frac{p+3}{7p(p+3)} = \frac{1}{9} \cdot \frac{1}{7p} = \frac{1}{63p}$, excluded values: $p \neq 7, -3$
17) $\frac{9}{n+5} \cdot \frac{(n-2)(n+7)}{(n+7)(n+5)} = \frac{9}{n+5} \cdot \frac{n-2}{n+5} = \frac{9(n-2)}{(n+5)^2}$, excluded values: $n \neq -5, -7$
18) $\frac{x^2+4x+4}{x^2+10x+16} \cdot \frac{x^2+10x+16}{x^2-64} = \frac{(x+2)^2}{(x+2)(x+8)} \cdot \frac{(x+2)(x+8)}{(x-8)(x+8)} = \frac{x+2}{x-8}$, excluded values: $x \neq -2, -8, 8$
19) $\frac{21b-28}{24-18b} \cdot \frac{b+7}{9b+63} = \frac{7(3b-4)}{6(4-3b)} \cdot \frac{b+7}{9(b+7)} = \frac{7(3b-4)}{6(4-3b)} \cdot \frac{1}{9} = \frac{7(3b-4)}{54(4-3b)} = \frac{7(-1)(4-3b)}{54(4-3b)} = -\frac{7}{54}$, excluded values: $b \neq \frac{4}{3}, -7$
20) $\frac{n-7}{3n+15} \cdot \frac{42+6n}{6n+18} = \frac{n-7}{3(n+5)} \cdot \frac{6(n+7)}{6(n+3)} = \frac{n-7}{3(n+5)} \cdot \frac{n+7}{n+3} = \frac{(n-7)(n+7)}{3(n+5)(n+3)} = \frac{n^2-49}{3(n+5)(n+3)}$, excluded values: $n \neq -5, -3$
Parent Tip: Review the logic above to help your child master the concept of multiplying rational expressions worksheet.
