(gelijknamig maken)
\(y = {1 \over x + 6} + 3\)
\(\text{} = {1 \over x + 6} + {3 \over 1}\)
\(\text{} = {1 \over x + 6} + {3 (x + 6) \over x + 6}\)

(haakjes uitwerken)
\(y = {1 + 3 (x + 6) \over x + 6}\)
\(\text{} = {1 + 3 x + 18 \over x + 6}\)
\(\text{} = {3 x + 19 \over x + 6}\)

(gelijknamig maken)
\(y = {6 \over x} - {4 x \over 1}\)
\(\text{} = {6 \over x} - {4 x ⋅ x \over x}\)

(herleiden)
\(y = {6 \over x} - {4 x^{2} \over x}\)
\(y = {6 - 4 x^{2} \over x}\)

(breuk vermenigvuldigen)
\(y = {9 x \over x - 1} ⋅ \frac{1}{3} ⋅ {x + 4 \over 1}\)
\(\text{} = {9 x ⋅ 1 ⋅ (x + 4) \over (x - 1) ⋅ 3 ⋅ 1}\)

(vereenvoudigen)
\(y = {9 x (x + 4) \over 3 (x - 1)}\)
\(y = {3 x (x + 4) \over x - 1}\)

(haakjes wegwerken)
\(y = {3 x^{2} + 12 x \over x - 1}\)

(balansmethode)
\(y - 2 = {5 \over x}\)

(wisseleigenschap, ofwel \({A \over B} = C\) geeft \({A \over C} = B \text{)}\)
\(x = {5 \over y - 2}\)

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {63 \over 7} ⋅ (5 x + 3) - 2\)

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

(haakjes wegwerken)
\(y = 45 x + 27 - 2\)
\(y = 45 x + 25\)

(balansmethode)
\({y \over 6 x + 4} = -2\)

(kruislings vermenigvuldigen)
\({y \over 6 x + 4} = {-2 \over 1}\)
\(y = -2 ⋅ (6 x + 4)\)

(haakjes wegwerken)
\(y = -12 x - 8\)

(kruislings vermenigvuldigen)
\({y \over 1} = {3 x - 27 \over 15}\)
\(3 x - 27 = 15 y\)

(balansmethode)
\(3 x = 15 y + 27\)
\(x = 5 y + 9\)

(uitdelen)
\(y = {9{,}5 x^{2} \over x} - {7 x \over x} + {5{,}5 \over x} - 6 x + 4\)
\(\text{} = 9{,}5 x - 7 + {5{,}5 \over x} - 6 x + 4\)

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