Gebroken formules herleiden

(gelijknamig maken)
\(y = {1 \over x - 1} + 6\)
\(\text{} = {1 \over x - 1} + {6 \over 1}\)
\(\text{} = {1 \over x - 1} + {6 (x - 1) \over x - 1}\)

(haakjes uitwerken)
\(y = {1 + 6 (x - 1) \over x - 1}\)
\(\text{} = {1 + 6 x - 6 \over x - 1}\)
\(\text{} = {6 x - 5 \over x - 1}\)

(gelijknamig maken)
\(y = {4 \over x} + {x \over 1}\)
\(\text{} = {4 \over x} + {x ⋅ x \over x}\)

(herleiden)
\(y = {4 \over x} + {x^{2} \over x}\)
\(y = {x^{2} + 4 \over x}\)

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {35 \over 7} ⋅ (2 x - 6) - 9\)

(breuk vereenvoudigen)
\(y = 5 ⋅ (2 x - 6) - 9\)

(haakjes wegwerken)
\(y = 10 x - 30 - 9\)
\(y = 10 x - 39\)

(breuk vermenigvuldigen)
\(y = {x + 2 \over 1} ⋅ {9 x \over x - 6} ⋅ \frac{2}{9}\)
\(\text{} = {(x + 2) ⋅ 9 x ⋅ 2 \over 1 ⋅ (x - 6) ⋅ 9}\)

(vereenvoudigen)
\(y = {18 x (x + 2) \over 9 (x - 6)}\)
\(y = {2 x (x + 2) \over x - 6}\)

(haakjes wegwerken)
\(y = {2 x^{2} + 4 x \over x - 6}\)

(uitdelen)
\(y = {7 x^{2} \over x} - {3 x \over x} + {4{,}5 \over x} - 8{,}5 x - 5\)
\(\text{} = 7 x - 3 + {4{,}5 \over x} - 8{,}5 x - 5\)

(herleiden)
\(y = -1{,}5 x - 8 + {4{,}5 \over x}\)

(balansmethode)
\(y - 6 = {2 \over x}\)

(wisseleigenschap, ofwel \({A \over B} = C\) geeft \({A \over C} = B \text{)}\)
\(x = {2 \over y - 6}\)

(kruislings vermenigvuldigen)
\({y \over 1} = {3 x - 6 \over 15}\)
\(3 x - 6 = 15 y\)

(balansmethode)
\(3 x = 15 y + 6\)
\(x = 5 y + 2\)

(balansmethode)
\({y \over 6 x + 3} = -2\)

(kruislings vermenigvuldigen)
\({y \over 6 x + 3} = {-2 \over 1}\)
\(y = -2 ⋅ (6 x + 3)\)

(haakjes wegwerken)
\(y = -12 x - 6\)

Kruislings vermenigvuldigen geeft
\(7 x + 8 = y (5 x + 1)\)
\(7 x + 8 = 5 x y + y\)

Termen met \(x\) naar links brengen geeft
\(-5 x y + 7 x = y - 8\)
\(x (-5 y + 7) = y - 8\)
\(x = {y - 8 \over -5 y + 7}\)