(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)
\(y = {1 - 2 (x + 3) \over x + 3}\)
\(\text{} = {1 - 2 x - 6 \over x + 3}\)
\(\text{} = {-2 x - 5 \over x + 3}\)

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

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

(breuk vermenigvuldigen)
\(y = \frac{7}{8} ⋅ {x + 3 \over 1} ⋅ {8 x \over x - 1}\)
\(\text{} = {7 ⋅ (x + 3) ⋅ 8 x \over 8 ⋅ 1 ⋅ (x - 1)}\)

(vereenvoudigen)
\(y = {56 x (x + 3) \over 8 (x - 1)}\)
\(y = {7 x (x + 3) \over x - 1}\)

(haakjes wegwerken)
\(y = {7 x^{2} + 21 x \over x - 1}\)

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

(wisseleigenschap, ofwel \({A \over B} = C\) geeft \({A \over C} = B \text{)}\)
\(x = {-3 \over y - 6}\)

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {8 \over 2} ⋅ (7 x - 9) + 3\)

(breuk vereenvoudigen)
\(y = 4 ⋅ (7 x - 9) + 3\)

(haakjes wegwerken)
\(y = 28 x - 36 + 3\)
\(y = 28 x - 33\)

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

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

(haakjes wegwerken)
\(y = 4 x - 24\)

(kruislings vermenigvuldigen)
\({y \over 1} = {2 x - 8 \over 16}\)
\(2 x - 8 = 16 y\)

(balansmethode)
\(2 x = 16 y + 8\)
\(x = 8 y + 4\)

(uitdelen)
\(y = {2{,}5 x^{2} \over x} + {5{,}5 x \over x} - {6 \over x} + 9 x + 3\)
\(\text{} = 2{,}5 x + 5{,}5 - {6 \over x} + 9 x + 3\)

(herleiden)
\(y = 11{,}5 x + 8{,}5 - {6 \over x}\)