Gebroken formules herleiden

(gelijknamig maken)
\(y = {1 \over x + 4} - 5\)
\(\text{} = {1 \over x + 4} - {5 \over 1}\)
\(\text{} = {1 \over x + 4} - {5 (x + 4) \over x + 4}\)

(haakjes uitwerken)
\(y = {1 - 5 (x + 4) \over x + 4}\)
\(\text{} = {1 - 5 x - 20 \over x + 4}\)
\(\text{} = {-5 x - 19 \over x + 4}\)

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

(herleiden)
\(y = {6 \over x} + {5 x^{2} \over x}\)
\(y = {5 x^{2} + 6 \over x}\)

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {18 \over 2} ⋅ (6 x + 1) - 7\)

(breuk vereenvoudigen)
\(y = 9 ⋅ (6 x + 1) - 7\)

(haakjes wegwerken)
\(y = 54 x + 9 - 7\)
\(y = 54 x + 2\)

(breuk vermenigvuldigen)
\(y = \frac{1}{2} ⋅ {x - 8 \over 1} ⋅ {6 x \over x - 1}\)
\(\text{} = {1 ⋅ (x - 8) ⋅ 6 x \over 2 ⋅ 1 ⋅ (x - 1)}\)

(vereenvoudigen)
\(y = {6 x (x - 8) \over 2 (x - 1)}\)
\(y = {3 x (x - 8) \over x - 1}\)

(haakjes wegwerken)
\(y = {3 x^{2} - 24 x \over x - 1}\)

(uitdelen)
\(y = {9{,}5 x^{2} \over x} - {5 x \over x} - {2 \over x} + 1{,}5 x + 3\)
\(\text{} = 9{,}5 x - 5 - {2 \over x} + 1{,}5 x + 3\)

(herleiden)
\(y = 11 x - 2 - {2 \over x}\)

(balansmethode)
\(y - 4 = {9 \over x}\)

(wisseleigenschap, ofwel \({A \over B} = C\) geeft \({A \over C} = B \text{)}\)
\(x = {9 \over y - 4}\)

(kruislings vermenigvuldigen)
\({y \over 1} = {2 x + 12 \over 14}\)
\(2 x + 12 = 14 y\)

(balansmethode)
\(2 x = 14 y - 12\)
\(x = 7 y - 6\)

(balansmethode)
\({y \over 4 x - 1} = -1\)

(kruislings vermenigvuldigen)
\({y \over 4 x - 1} = {-1 \over 1}\)
\(y = -1 ⋅ (4 x - 1)\)

(haakjes wegwerken)
\(y = -4 x + 1\)

Kruislings vermenigvuldigen geeft
\(9 x - 1 = y (-2 x + 5)\)
\(9 x - 1 = -2 x y + 5 y\)

Termen met \(x\) naar links brengen geeft
\(2 x y + 9 x = 5 y + 1\)
\(x (2 y + 9) = 5 y + 1\)
\(x = {5 y + 1 \over 2 y + 9}\)