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

(haakjes uitwerken)
\(y = {1 - 3 (x + 1) \over x + 1}\)
\(\text{} = {1 - 3 x - 3 \over x + 1}\)
\(\text{} = {-3 x - 2 \over x + 1}\)

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

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

(breuk vermenigvuldigen)
\(y = {7 x \over x + 4} ⋅ \frac{6}{7} ⋅ {x - 2 \over 1}\)
\(\text{} = {7 x ⋅ 6 ⋅ (x - 2) \over (x + 4) ⋅ 7 ⋅ 1}\)

(vereenvoudigen)
\(y = {42 x (x - 2) \over 7 (x + 4)}\)
\(y = {6 x (x - 2) \over x + 4}\)

(haakjes wegwerken)
\(y = {6 x^{2} - 12 x \over x + 4}\)

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

(wisseleigenschap, ofwel \({A \over B} = C\) geeft \({A \over C} = B \text{)}\)
\(x = {-4 \over y - 3}\)

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {32 \over 4} ⋅ (7 x + 5) - 9\)

(breuk vereenvoudigen)
\(y = 8 ⋅ (7 x + 5) - 9\)

(haakjes wegwerken)
\(y = 56 x + 40 - 9\)
\(y = 56 x + 31\)

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

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

(haakjes wegwerken)
\(y = 5 x + 1\)

(kruislings vermenigvuldigen)
\({y \over 1} = {3 x - 6 \over 24}\)
\(3 x - 6 = 24 y\)

(balansmethode)
\(3 x = 24 y + 6\)
\(x = 8 y + 2\)

(uitdelen)
\(y = {9 x^{2} \over x} - {6 x \over x} - {8 \over x} + 4{,}5 x + 1{,}5\)
\(\text{} = 9 x - 6 - {8 \over x} + 4{,}5 x + 1{,}5\)

(herleiden)
\(y = 13{,}5 x - 4{,}5 - {8 \over x}\)