Gebroken formules herleiden

(gelijknamig maken)
\(y = {1 \over x + 6} + 5\)
\(\text{} = {1 \over x + 6} + {5 \over 1}\)
\(\text{} = {1 \over x + 6} + {5 (x + 6) \over x + 6}\)

(haakjes uitwerken)
\(y = {1 + 5 (x + 6) \over x + 6}\)
\(\text{} = {1 + 5 x + 30 \over x + 6}\)
\(\text{} = {5 x + 31 \over x + 6}\)

(gelijknamig maken)
\(y = {4 \over x} + {6 x \over 1}\)
\(\text{} = {4 \over x} + {6 x ⋅ x \over x}\)

(herleiden)
\(y = {4 \over x} + {6 x^{2} \over x}\)
\(y = {6 x^{2} + 4 \over x}\)

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {36 \over 9} ⋅ (7 x + 3) - 5\)

(breuk vereenvoudigen)
\(y = 4 ⋅ (7 x + 3) - 5\)

(haakjes wegwerken)
\(y = 28 x + 12 - 5\)
\(y = 28 x + 7\)

(breuk vermenigvuldigen)
\(y = {9 x \over x + 8} ⋅ {x + 6 \over 1} ⋅ \frac{1}{3}\)
\(\text{} = {9 x ⋅ (x + 6) ⋅ 1 \over (x + 8) ⋅ 1 ⋅ 3}\)

(vereenvoudigen)
\(y = {9 x (x + 6) \over 3 (x + 8)}\)
\(y = {3 x (x + 6) \over x + 8}\)

(haakjes wegwerken)
\(y = {3 x^{2} + 18 x \over x + 8}\)

(uitdelen)
\(y = {2 x^{2} \over x} - {8{,}5 x \over x} - {3 \over x} + 4 x + 1{,}5\)
\(\text{} = 2 x - 8{,}5 - {3 \over x} + 4 x + 1{,}5\)

(herleiden)
\(y = 6 x - 7 - {3 \over x}\)

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

(wisseleigenschap, ofwel \({A \over B} = C\) geeft \({A \over C} = B \text{)}\)
\(x = {2 \over y - 8}\)

(kruislings vermenigvuldigen)
\({y \over 1} = {3 x - 27 \over 24}\)
\(3 x - 27 = 24 y\)

(balansmethode)
\(3 x = 24 y + 27\)
\(x = 8 y + 9\)

(balansmethode)
\({y \over 7 x - 8} = -1\)

(kruislings vermenigvuldigen)
\({y \over 7 x - 8} = {-1 \over 1}\)
\(y = -1 ⋅ (7 x - 8)\)

(haakjes wegwerken)
\(y = -7 x + 8\)

Kruislings vermenigvuldigen geeft
\(9 x - 4 = y (-8 x + 2)\)
\(9 x - 4 = -8 x y + 2 y\)

Termen met \(x\) naar links brengen geeft
\(8 x y + 9 x = 2 y + 4\)
\(x (8 y + 9) = 2 y + 4\)
\(x = {2 y + 4 \over 8 y + 9}\)