((x+1)^2+14)/(4x+5)=n

解

\frac{( x + 1 ) ^{2} + 14}{4 x + 5} = n

x = - 1 + 2 n + 4 n^{2} + n - 14, x = - 1 + 2 n - 4 n^{2} + n - 14

解答ステップ

\frac{( x + 1 ) ^{2} + 14}{4 x + 5} = n

簡素化

\frac{( x + 1 ) ^{2} + 14}{4 x + 5} : \frac{x ^{2} + 2 x + 15}{4 x + 5}

\frac{x ^{2} + 2 x + 15}{4 x + 5} = n

以下で両辺を乗じる:

4 x + 5

x^{2} + 2 x + 15 = n (4 x + 5)

解く

x^{2} + 2 x + 15 = n (4 x + 5) : x = - 1 + 2 n + 4 n^{2} + n - 14, x = - 1 + 2 n - 4 n^{2} + n - 14

x = - 1 + 2 n + 4 n^{2} + n - 14, x = - 1 + 2 n - 4 n^{2} + n - 14