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)
\(y = {2 \over x} - {3 x \over 1}\)
\(\text{} = {2 \over x} - {3 x ⋅ x \over x}\)

(herleiden)
\(y = {2 \over x} - {3 x^{2} \over x}\)
\(y = {2 - 3 x^{2} \over x}\)

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {54 \over 9} ⋅ (3 x - 2) + 7\)

(breuk vereenvoudigen)
\(y = 6 ⋅ (3 x - 2) + 7\)

(haakjes wegwerken)
\(y = 18 x - 12 + 7\)
\(y = 18 x - 5\)

(breuk vermenigvuldigen)
\(y = \frac{2}{3} ⋅ {9 x \over x - 7} ⋅ {x + 6 \over 1}\)
\(\text{} = {2 ⋅ 9 x ⋅ (x + 6) \over 3 ⋅ (x - 7) ⋅ 1}\)

(vereenvoudigen)
\(y = {18 x (x + 6) \over 3 (x - 7)}\)
\(y = {6 x (x + 6) \over x - 7}\)

(haakjes wegwerken)
\(y = {6 x^{2} + 36 x \over x - 7}\)

(uitdelen)
\(y = {5 x^{2} \over x} + {6 x \over x} - {3{,}5 \over x} - x + 3{,}5\)
\(\text{} = 5 x + 6 - {3{,}5 \over x} - x + 3{,}5\)

(herleiden)
\(y = 4 x + 9{,}5 - {3{,}5 \over x}\)

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

(wisseleigenschap, ofwel \({A \over B} = C\) geeft \({A \over C} = B \text{)}\)
\(x = {4 \over y - 2}\)

(kruislings vermenigvuldigen)
\({y \over 1} = {3 x + 12 \over 6}\)
\(3 x + 12 = 6 y\)

(balansmethode)
\(3 x = 6 y - 12\)
\(x = 2 y - 4\)

(balansmethode)
\({y \over 2 x + 1} = 3\)

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

(haakjes wegwerken)
\(y = 6 x + 3\)

Kruislings vermenigvuldigen geeft
\(3 x - 7 = y (-9 x + 8)\)
\(3 x - 7 = -9 x y + 8 y\)

Termen met \(x\) naar links brengen geeft
\(9 x y + 3 x = 8 y + 7\)
\(x (9 y + 3) = 8 y + 7\)
\(x = {8 y + 7 \over 9 y + 3}\)