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\({6 \over x}:{4 \over y}={6 \over x}⋅{y \over 4}={6y \over 4x}={3y \over 2x}\)

\({1 \over 4}:a={1 \over 4}:{a \over 1}={1 \over 4}⋅{1 \over a}={1 \over 4a}\)

\({1 \over 7}:{p-8q \over q}={1 \over 7}⋅{q \over p-8q}={q \over 7(p-8q)}={q \over 7p-56q}\)

\({2 \over 7x}+{9 \over 7x}={11 \over 7x}\)

\({3 \over a}-{2 \over 6a}={18 \over 6a}-{2 \over 6a}={16 \over 6a}={8 \over 3a}\)

\({4 \over 9a}-{2 \over 5b}={20b \over 45ab}-{18a \over 45ab}={20b-18a \over 45ab}\)

\(6+{2 \over 7p}={6 \over 1}+{2 \over 7p}={42p \over 7p}+{2 \over 7p}={42p+2 \over 7p}\)

\(8a+{3 \over 2a}={8a \over 1}⋅{2a \over 2a}+{3 \over 2a}={16a^2 \over 2a}+{3 \over 2a}={16a^2+3 \over 2a}\)

\({5x \over y}-{6 \over 7y}={35x \over 7y}-{6 \over 7y}={35x-6 \over 7y}\)

\({7y \over 6x}-{9x \over 3y}={7y^2 \over 6xy}-{18x^2 \over 6xy}={-18x^2+7y^2 \over 6xy}\)

\({6x \over 7}+{x-5 \over 4}={24x \over 28}+{7(x-5) \over 28}={24x+7(x-5) \over 28}={31x-35 \over 28}\)

\({2p+9 \over 4p+5}-7={2p+9 \over 4p+5}-{7(4p+5) \over 4p+5}={2p+9-7(4p+5) \over 4p+5}={2p+9-28p-35 \over 4p+5}={-26p-26 \over 4p+5}\)

\({8 \over x}⋅{3 \over y}={24 \over xy}\)

\({a \over 7}⋅-{4 \over b}=-{4a \over 7b}\)

\({7 \over 4}⋅a={7a \over 4}\)

\({3y \over x}⋅{x-7 \over 9}={3y(x-7) \over 9x}={y(x-7) \over 3x}={xy-7y \over 3x}\)

\({6a^2+9a-30 \over 3a}={6a^2 \over 3a}+{9a \over 3a}-{30 \over 3a}=2a+3-{10 \over a}\)

\({2x^2-8x-5 \over x^2}={2x^2 \over x^2}-{8x \over x^2}-{5 \over x^2}=2-{8 \over x}-{5 \over x^2}\)

\({4a \over a}={4 \over 1}=4\)

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

\({12a \over 15a}=\frac{4}{5}\)

\({21x \over -3x}=-7\)

\({8xy \over 14xz}={4y \over 7z}\)

\({4b \over 10ab}={2 \over 5a}\)

\({35pqr \over -5qr}=-7p\)

\({4xy \over y}+{5xz \over z}=4x+5x=9x\)