(gelijknamig maken)
\(y = {1 \over x - 4} - 3\)
\(\text{} = {1 \over x - 4} - {3 \over 1}\)
\(\text{} = {1 \over x - 4} - {3 (x - 4) \over x - 4}\)

(haakjes uitwerken)
\(y = {1 - 3 (x - 4) \over x - 4}\)
\(\text{} = {1 - 3 x + 12 \over x - 4}\)
\(\text{} = {-3 x + 13 \over x - 4}\)

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

(herleiden)
\(y = {1 \over x} - {6 x^{2} \over x}\)
\(y = {1 - 6 x^{2} \over x}\)

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

(vereenvoudigen)
\(y = {6 x (x + 1) \over 6 (x + 5)}\)
\(y = {x (x + 1) \over x + 5}\)

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

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

(wisseleigenschap, ofwel \({A \over B} = C\) geeft \({A \over C} = B \text{)}\)
\(x = {5 \over y - 6}\)

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {18 \over 6} ⋅ (9 x + 2) + 5\)

(breuk vereenvoudigen)
\(y = 3 ⋅ (9 x + 2) + 5\)

(haakjes wegwerken)
\(y = 27 x + 6 + 5\)
\(y = 27 x + 11\)

(balansmethode)
\({y \over 4 x - 3} = 1\)

(kruislings vermenigvuldigen)
\({y \over 4 x - 3} = {1 \over 1}\)
\(y = 1 ⋅ (4 x - 3)\)

(haakjes wegwerken)
\(y = 4 x - 3\)

(kruislings vermenigvuldigen)
\({y \over 1} = {3 x - 21 \over 6}\)
\(3 x - 21 = 6 y\)

(balansmethode)
\(3 x = 6 y + 21\)
\(x = 2 y + 7\)

(uitdelen)
\(y = {6{,}5 x^{2} \over x} + {5 x \over x} - {9 \over x} - 6{,}5 x - 8\)
\(\text{} = 6{,}5 x + 5 - {9 \over x} - 6{,}5 x - 8\)

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