(gelijknamig maken)
\(y = {1 \over x + 2} + 5\)
\(\text{} = {1 \over x + 2} + {5 \over 1}\)
\(\text{} = {1 \over x + 2} + {5 (x + 2) \over x + 2}\)

(haakjes uitwerken)
\(y = {1 + 5 (x + 2) \over x + 2}\)
\(\text{} = {1 + 5 x + 10 \over x + 2}\)
\(\text{} = {5 x + 11 \over x + 2}\)

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

(herleiden)
\(y = {3 \over x} + {4 x^{2} \over x}\)
\(y = {4 x^{2} + 3 \over x}\)

(breuk vermenigvuldigen)
\(y = \frac{1}{2} ⋅ {x + 1 \over 1} ⋅ {6 x \over x + 8}\)
\(\text{} = {1 ⋅ (x + 1) ⋅ 6 x \over 2 ⋅ 1 ⋅ (x + 8)}\)

(vereenvoudigen)
\(y = {6 x (x + 1) \over 2 (x + 8)}\)
\(y = {3 x (x + 1) \over x + 8}\)

(haakjes wegwerken)
\(y = {3 x^{2} + 3 x \over x + 8}\)

(balansmethode)
\(y - 3 = {8 \over x}\)

(wisseleigenschap, ofwel \({A \over B} = C\) geeft \({A \over C} = B \text{)}\)
\(x = {8 \over y - 3}\)

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {48 \over 8} ⋅ (2 x - 7) + 9\)

(breuk vereenvoudigen)
\(y = 6 ⋅ (2 x - 7) + 9\)

(haakjes wegwerken)
\(y = 12 x - 42 + 9\)
\(y = 12 x - 33\)

(balansmethode)
\({y \over 8 x - 4} = -1\)

(kruislings vermenigvuldigen)
\({y \over 8 x - 4} = {-1 \over 1}\)
\(y = -1 ⋅ (8 x - 4)\)

(haakjes wegwerken)
\(y = -8 x + 4\)

(kruislings vermenigvuldigen)
\({y \over 1} = {3 x - 18 \over 21}\)
\(3 x - 18 = 21 y\)

(balansmethode)
\(3 x = 21 y + 18\)
\(x = 7 y + 6\)

(uitdelen)
\(y = {5 x^{2} \over x} + {6 x \over x} + {1 \over x} + 3{,}5 x + 8{,}5\)
\(\text{} = 5 x + 6 + {1 \over x} + 3{,}5 x + 8{,}5\)

(herleiden)
\(y = 8{,}5 x + 14{,}5 + {1 \over x}\)