Breuken herleiden

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

\(-{5 \over 6} : x = -{5 \over 6} : {x \over 1} = -{5 \over 6} ⋅ {1 \over x} = -{5 \over 6 x}\)

\({3 \over 2} : {a - 8 b \over b} = {3 \over 2} ⋅ {b \over a - 8 b} = {3 b \over 2 (a - 8 b)} = {3 b \over 2 a - 16 b}\)

\({9 \over 3 p} + {8 \over 3 p} = {17 \over 3 p}\)

\({8 \over x} - {6 \over 5 x} = {40 \over 5 x} - {6 \over 5 x} = {34 \over 5 x}\)

\({5 \over 3 p} - {7 \over 9 q} = {15 q \over 9 p q} - {7 p \over 9 p q} = {15 q - 7 p \over 9 p q}\)

\(9 - {2 \over 3 x} = {9 \over 1} - {2 \over 3 x} = {27 x \over 3 x} - {2 \over 3 x} = {27 x - 2 \over 3 x}\)

\(4 x + {9 \over 2 x} = {4 x \over 1} ⋅ {2 x \over 2 x} + {9 \over 2 x} = {8 x^{2} \over 2 x} + {9 \over 2 x} = {8 x^{2} + 9 \over 2 x}\)

\({8 x \over y} - {9 \over 6 y} = {48 x \over 6 y} - {9 \over 6 y} = {48 x - 9 \over 6 y} = {16 x - 3 \over 2 y}\)

\({5 y \over 8 x} + {9 x \over 4 y} = {5 y^{2} \over 8 x y} + {18 x^{2} \over 8 x y} = {18 x^{2} + 5 y^{2} \over 8 x y}\)

\({7 x \over 3} + {x - 4 \over 5} = {35 x \over 15} + {3 (x - 4) \over 15} = {35 x + 3 (x - 4) \over 15} = {38 x - 12 \over 15}\)

\({-9 p - 3 \over 6 p - 5} - 8 = {-9 p - 3 \over 6 p - 5} - {8 (6 p - 5) \over 6 p - 5} = {-9 p - 3 - 8 (6 p - 5) \over 6 p - 5} = {-9 p - 3 - 48 p + 40 \over 6 p - 5} = {-57 p + 37 \over 6 p - 5}\)

\({3 x^{2} - 6 x + 90 \over 3 x} = {3 x^{2} \over 3 x} - {6 x \over 3 x} + {90 \over 3 x} = x - 2 + {30 \over x}\)

\({6 a^{2} - 3 a + 4 \over 2 a^{2}} = {6 a^{2} \over 2 a^{2}} - {3 a \over 2 a^{2}} + {4 \over 2 a^{2}} = 3 - {3 \over 2 a} + {2 \over a^{2}}\)

\({5 x \over x} = {5 \over 1} = 5\)

\({a \over 5 a} = {1 \over 5}\)

\({-15 p \over -27 p} = \frac{5}{9}\)

\({32 a \over 4 a} = 8\)

\({4 p q \over 18 p r} = {2 q \over 9 r}\)

\({-6 b \over 27 a b} = -{2 \over 9 a}\)

\({-8 x y z \over -2 y z} = 4 x\)

\({7 p q \over q} + {3 p r \over r} = 7 p + 3 p = 10 p\)

\({4 \over p} ⋅ -{3 \over q} = -{12 \over p q}\)

\({a \over 9} ⋅ -{3 \over b} = -{3 a \over 9 b} = -{a \over 3 b}\)

\(-{6 \over 7} ⋅ x = -{6 x \over 7}\)

\({6 q \over p} ⋅ {p + 9 \over 7} = {6 q (p + 9) \over 7 p} = {6 p q + 54 q \over 7 p}\)