Gebroken formules herleiden

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

(haakjes uitwerken)
\(y = {1 + 4 (x + 3) \over x + 3}\)
\(\text{} = {1 + 4 x + 12 \over x + 3}\)
\(\text{} = {4 x + 13 \over x + 3}\)

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

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

(\({A \over B} ⋅ C = {C \over B} ⋅ A\) geeft)
\(y = {63 \over 9} ⋅ (4 x + 3) - 2\)

(breuk vereenvoudigen)
\(y = 7 ⋅ (4 x + 3) - 2\)

(haakjes wegwerken)
\(y = 28 x + 21 - 2\)
\(y = 28 x + 19\)

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

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

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

(uitdelen)
\(y = {x^{2} \over x} + {9 x \over x} + {7{,}5 \over x} - 8 x - 3{,}5\)
\(\text{} = x + 9 + {7{,}5 \over x} - 8 x - 3{,}5\)

(herleiden)
\(y = -7 x + 5{,}5 + {7{,}5 \over x}\)

(balansmethode)
\(y - 5 = {7 \over x}\)

(wisseleigenschap, ofwel \({A \over B} = C\) geeft \({A \over C} = B \text{)}\)
\(x = {7 \over y - 5}\)

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

(balansmethode)
\(2 x = 6 y - 2\)
\(x = 3 y - 1\)

(balansmethode)
\({y \over 5 x - 8} = 6\)

(kruislings vermenigvuldigen)
\({y \over 5 x - 8} = {6 \over 1}\)
\(y = 6 ⋅ (5 x - 8)\)

(haakjes wegwerken)
\(y = 30 x - 48\)

Kruislings vermenigvuldigen geeft
\(5 x - 9 = y (-3 x - 2)\)
\(5 x - 9 = -3 x y - 2 y\)

Termen met \(x\) naar links brengen geeft
\(3 x y + 5 x = -2 y + 9\)
\(x (3 y + 5) = -2 y + 9\)
\(x = {-2 y + 9 \over 3 y + 5}\)