What is the answer to solvefor u, 1/u+1/v = 1/f ?

The answer to solvefor u, 1/u+1/v = 1/f is u=-(vf)/(f-v);\quad v\ne f

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solvefor u, 1/u+1/v = 1/f

solve for

u, \frac{1}{u} + \frac{1}{v} = \frac{1}{f}

u = - \frac{v f}{f - v}; v \neq = f

Solution steps

\frac{1}{u} + \frac{1}{v} = \frac{1}{f}

Multiply by LCM

v f + u f = uv

Move

v f

to the right side

u f = uv - v f

Move

uv

to the left side

u f - uv = - v f

Factor

u f - uv : u (f - v)

u (f - v) = - v f

Divide both sides by

f - v; v \neq = f

u = - \frac{v f}{f - v}; v \neq = f

2 x = \frac{1}{3 x ^{2}}

\frac{x + 1}{x} = \frac{29}{10}

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

a, \frac{1}{a} + \frac{2}{b} = \frac{1}{3}

\frac{1.2}{43} = \frac{4.8}{x}

What is the answer to solvefor u, 1/u+1/v = 1/f ?
The answer to solvefor u, 1/u+1/v = 1/f is u=-(vf)/(f-v);\quad v\ne f