What is the answer to x-1/a = x/a ?

The answer to x-1/a = x/a is x= 1/(a-1);\quad a\ne 0,a\ne 1

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x-1/a = x/a

x - \frac{1}{a} = \frac{x}{a}

x = \frac{1}{a - 1}; a \neq = 0, a \neq = 1

Solution steps

x - \frac{1}{a} = \frac{x}{a}

Move

\frac{1}{a}

to the right side

x = \frac{x + 1}{a}

Multiply both sides by

a

x a = x + 1; a \neq = 0

Move

x

to the left side

x a - x = 1; a \neq = 0

Factor

x a - x : x (a - 1)

x (a - 1) = 1; a \neq = 0

Divide both sides by

a - 1; a \neq = 0, a \neq = 1

x = \frac{1}{a - 1}; a \neq = 0, a \neq = 1

\frac{3 y + 4}{2} + \frac{2 y - 5}{3} = \frac{31}{2}

\frac{3}{4} (\frac{1}{4} x + 8) - (\frac{1}{2} x + 2) = \frac{3}{8} (4 - x) - \frac{1}{4} x

\frac{x + 1}{2} + 3 x = \frac{5}{4}

x^{2} + 81 = x^{2} + 20 x + 100

\frac{2}{5} w = 15

What is the answer to x-1/a = x/a ?
The answer to x-1/a = x/a is x= 1/(a-1);\quad a\ne 0,a\ne 1