(gelijknamig maken)
\(y = {1 \over x + 3} + 2\)
\(\text{} = {1 \over x + 3} + {2 \over 1}\)
\(\text{} = {1 \over x + 3} + {2 (x + 3) \over x + 3}\)

(haakjes uitwerken)
\(y = {1 + 2 (x + 3) \over x + 3}\)
\(\text{} = {1 + 2 x + 6 \over x + 3}\)
\(\text{} = {2 x + 7 \over x + 3}\)

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {42 \over 6} ⋅ (4 x - 1) + 8\)

(breuk vereenvoudigen)
\(y = 7 ⋅ (4 x - 1) + 8\)

(haakjes wegwerken)
\(y = 28 x - 7 + 8\)
\(y = 28 x + 1\)

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

(herleiden)
\(y = {1 \over x} + {4 x^{2} \over x}\)
\(y = {4 x^{2} + 1 \over x}\)

(breuk vermenigvuldigen)
\(y = \frac{1}{6} ⋅ {6 x \over x - 8} ⋅ {x - 5 \over 1}\)
\(\text{} = {1 ⋅ 6 x ⋅ (x - 5) \over 6 ⋅ (x - 8) ⋅ 1}\)

(vereenvoudigen)
\(y = {6 x (x - 5) \over 6 (x - 8)}\)
\(y = {x (x - 5) \over x - 8}\)

(haakjes wegwerken)
\(y = {x^{2} - 5 x \over x - 8}\)

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

(herleiden)
\(y = -2{,}5 x + 9{,}5 - {8 \over x}\)

Kruislings vermenigvuldigen geeft
\(6 x + 9 = y (8 x - 2)\)
\(6 x + 9 = 8 x y - 2 y\)

Termen met \(x\) naar links brengen geeft
\(-8 x y + 6 x = -2 y - 9\)
\(x (-8 y + 6) = -2 y - 9\)
\(x = {-2 y - 9 \over -8 y + 6}\)

(balansmethode)
\(y - 8 = -{5 \over x}\)

(wisseleigenschap, ofwel \({A \over B} = C\) geeft \({A \over C} = B \text{)}\)
\(x = {-5 \over y - 8}\)

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

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

(haakjes wegwerken)
\(y = -18 x + 6\)

(kruislings vermenigvuldigen)
\({y \over 1} = {2 x + 16 \over 18}\)
\(2 x + 16 = 18 y\)

(balansmethode)
\(2 x = 18 y - 16\)
\(x = 9 y - 8\)