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

(haakjes uitwerken)
\(y = {1 + (x + 3) \over x + 3}\)
\(\text{} = {1 + x + 3 \over x + 3}\)
\(\text{} = {x + 4 \over x + 3}\)

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {12 \over 4} ⋅ (6 x + 2) - 8\)

(breuk vereenvoudigen)
\(y = 3 ⋅ (6 x + 2) - 8\)

(haakjes wegwerken)
\(y = 18 x + 6 - 8\)
\(y = 18 x - 2\)

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

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

(breuk vermenigvuldigen)
\(y = {x - 8 \over 1} ⋅ \frac{1}{7} ⋅ {7 x \over x + 5}\)
\(\text{} = {(x - 8) ⋅ 1 ⋅ 7 x \over 1 ⋅ 7 ⋅ (x + 5)}\)

(vereenvoudigen)
\(y = {7 x (x - 8) \over 7 (x + 5)}\)
\(y = {x (x - 8) \over x + 5}\)

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

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

(herleiden)
\(y = 3{,}5 x - 9{,}5 - {1 \over x}\)

Kruislings vermenigvuldigen geeft
\(6 x + 4 = y (-5 x + 9)\)
\(6 x + 4 = -5 x y + 9 y\)

Termen met \(x\) naar links brengen geeft
\(5 x y + 6 x = 9 y - 4\)
\(x (5 y + 6) = 9 y - 4\)
\(x = {9 y - 4 \over 5 y + 6}\)

(balansmethode)
\(y - 3 = -{8 \over x}\)

(wisseleigenschap, ofwel \({A \over B} = C\) geeft \({A \over C} = B \text{)}\)
\(x = {-8 \over y - 3}\)

(balansmethode)
\({y \over 8 x + 5} = 7\)

(kruislings vermenigvuldigen)
\({y \over 8 x + 5} = {7 \over 1}\)
\(y = 7 ⋅ (8 x + 5)\)

(haakjes wegwerken)
\(y = 56 x + 35\)

(kruislings vermenigvuldigen)
\({y \over 1} = {3 x - 24 \over 18}\)
\(3 x - 24 = 18 y\)

(balansmethode)
\(3 x = 18 y + 24\)
\(x = 6 y + 8\)