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\({6 \over a}:{9 \over b}={6 \over a}⋅{b \over 9}={6b \over 9a}={2b \over 3a}\)

\(-{4 \over 9}:x=-{4 \over 9}:{x \over 1}=-{4 \over 9}⋅{1 \over x}=-{4 \over 9x}\)

\({1 \over 6}:{p-8q \over q}={1 \over 6}⋅{q \over p-8q}={q \over 6(p-8q)}={q \over 6p-48q}\)

\({7 \over 8x}+{9 \over 8x}={16 \over 8x}={2 \over x}\)

\({9 \over a}+{4 \over 5a}={45 \over 5a}+{4 \over 5a}={49 \over 5a}\)

\({4 \over 2p}-{8 \over 6q}={12q \over 6pq}-{8p \over 6pq}={12q-8p \over 6pq}={6q-4p \over 3pq}\)

\(2+{9 \over 4a}={2 \over 1}+{9 \over 4a}={8a \over 4a}+{9 \over 4a}={8a+9 \over 4a}\)

\(5x+{4 \over 9x}={5x \over 1}⋅{9x \over 9x}+{4 \over 9x}={45x^2 \over 9x}+{4 \over 9x}={45x^2+4 \over 9x}\)

\({8a \over b}+{4 \over 9b}={72a \over 9b}+{4 \over 9b}={72a+4 \over 9b}\)

\({4y \over 9x}+{7x \over 5y}={20y^2 \over 45xy}+{63x^2 \over 45xy}={63x^2+20y^2 \over 45xy}\)

\({7x \over 9}+{x+4 \over 2}={14x \over 18}+{9(x+4) \over 18}={14x+9(x+4) \over 18}={23x+36 \over 18}\)

\({-4p+6 \over -8p+1}+3={-4p+6 \over -8p+1}-{-3(-8p+1) \over -8p+1}={-4p+6+3(-8p+1) \over -8p+1}={-4p+6-24p+3 \over -8p+1}={-28p+9 \over -8p+1}\)

\({5 \over p}⋅-{9 \over q}=-{45 \over pq}\)

\({x \over 9}⋅{7 \over y}={7x \over 9y}\)

\({9 \over 7}⋅a={9a \over 7}\)

\({6q \over p}⋅{p+2 \over 9}={6q(p+2) \over 9p}={2q(p+2) \over 3p}={2pq+4q \over 3p}\)

\({x^2+3x-20 \over x}={x^2 \over x}+{3x \over x}-{20 \over x}=x+3-{20 \over x}\)

\({8a^2-4a-9 \over a^2}={8a^2 \over a^2}-{4a \over a^2}-{9 \over a^2}=8-{4 \over a}-{9 \over a^2}\)

\({3a \over a}={3 \over 1}=3\)

\({x \over 6x}={1 \over 6}\)

\({-8a \over -20a}=\frac{2}{5}\)

\({40x \over 5x}=8\)

\({-25pq \over 40pr}=-{5q \over 8r}\)

\({-24b \over 28ab}=-{6 \over 7a}\)

\({-12xyz \over 3yz}=-4x\)

\({6ab \over b}-{3ac \over c}=6a-3a=3a\)