What is the answer to solvefor u,S= u/(au+v) ?

The answer to solvefor u,S= u/(au+v) is u=-(vS)/(aS-1);\quad a\ne 1/S

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solvefor u,S= u/(au+v)

solve for

u, S = \frac{u}{a u + v}

u = - \frac{v S}{a S - 1}; a \neq = \frac{1}{S}

Solution steps

S = \frac{u}{a u + v}

Multiply both sides by

a u + v

S (a u + v) = u

Expand

S (a u + v) : a u S + v S

a u S + v S = u

Move

v S

to the right side

a u S = u - v S

Move

u

to the left side

a u S - u = - v S

Factor

a u S - u : u (a S - 1)

u (a S - 1) = - v S

Divide both sides by

a S - 1; a \neq = \frac{1}{S}

u = - \frac{v S}{a S - 1}; a \neq = \frac{1}{S}

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

\frac{x}{x + 2} = \frac{x - 2}{x - 4}

n, K = \frac{a}{b ( c + n )}

x - 1 = \frac{- 4 x}{x + 1} + 5

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

What is the answer to solvefor u,S= u/(au+v) ?
The answer to solvefor u,S= u/(au+v) is u=-(vS)/(aS-1);\quad a\ne 1/S