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

(haakjes uitwerken)
\(y = {1 + 6 (x - 5) \over x - 5}\)
\(\text{} = {1 + 6 x - 30 \over x - 5}\)
\(\text{} = {6 x - 29 \over x - 5}\)

(gelijknamig maken)
\(y = {2 \over x} - {4 x \over 1}\)
\(\text{} = {2 \over x} - {4 x ⋅ x \over x}\)

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

(breuk vermenigvuldigen)
\(y = {5 x \over x + 3} ⋅ {x + 4 \over 1} ⋅ \frac{4}{5}\)
\(\text{} = {5 x ⋅ (x + 4) ⋅ 4 \over (x + 3) ⋅ 1 ⋅ 5}\)

(vereenvoudigen)
\(y = {20 x (x + 4) \over 5 (x + 3)}\)
\(y = {4 x (x + 4) \over x + 3}\)

(haakjes wegwerken)
\(y = {4 x^{2} + 16 x \over x + 3}\)

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

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

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {18 \over 9} ⋅ (8 x + 4) + 1\)

(breuk vereenvoudigen)
\(y = 2 ⋅ (8 x + 4) + 1\)

(haakjes wegwerken)
\(y = 16 x + 8 + 1\)
\(y = 16 x + 9\)

(balansmethode)
\({y \over 2 x + 7} = 6\)

(kruislings vermenigvuldigen)
\({y \over 2 x + 7} = {6 \over 1}\)
\(y = 6 ⋅ (2 x + 7)\)

(haakjes wegwerken)
\(y = 12 x + 42\)

(kruislings vermenigvuldigen)
\({y \over 1} = {2 x - 6 \over 12}\)
\(2 x - 6 = 12 y\)

(balansmethode)
\(2 x = 12 y + 6\)
\(x = 6 y + 3\)

(uitdelen)
\(y = {2{,}5 x^{2} \over x} + {x \over x} - {6{,}5 \over x} + 9 x + 4\)
\(\text{} = 2{,}5 x + 1 - {6{,}5 \over x} + 9 x + 4\)

(herleiden)
\(y = 11{,}5 x + 5 - {6{,}5 \over x}\)