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

The answer to solvefor u,s= u/(au+v) is u=-(sv)/(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{s v}{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 + s v

a u s + s v = u

Move

s v

to the right side

a u s = u - s v

Move

u

to the left side

a u s - u = - s v

Factor

a u s - u : u (a s - 1)

u (a s - 1) = - s v

Divide both sides by

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

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

3 + \frac{2}{3 x} = \frac{6}{x}

\frac{6}{x} + 1 = 5

\frac{1}{x - 8} = - \frac{1}{x - 9}

x + \frac{1}{x - 3} = 5

\frac{6}{k - 1} = \frac{8}{k - 6}

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