x/a-a/x =x-a

解

\frac{x}{a} - \frac{a}{x} = x - a

x = \frac{- a ^{2} + a a ^{2} + 4 ( 1 - a )}{2 ( 1 - a )}, x = \frac{- a ^{2} - a a ^{2} + 4 ( 1 - a )}{2 ( 1 - a )}; a \neq = 1

解答ステップ

\frac{x}{a} - \frac{a}{x} = x - a

LCMで乗じる

x^{2} - a^{2} = a x^{2} - a^{2} x

解く

x^{2} - a^{2} = a x^{2} - a^{2} x : x = \frac{- a ^{2} + a a ^{2} + 4 ( 1 - a )}{2 ( 1 - a )}, x = \frac{- a ^{2} - a a ^{2} + 4 ( 1 - a )}{2 ( 1 - a )}; a \neq = 1

x = \frac{- a ^{2} + a a ^{2} + 4 ( 1 - a )}{2 ( 1 - a )}, x = \frac{- a ^{2} - a a ^{2} + 4 ( 1 - a )}{2 ( 1 - a )}; a \neq = 1