What is the answer to solvefor a, 1/a+1/b =c ?

The answer to solvefor a, 1/a+1/b =c is a=-b/(1-bc);\quad b\ne 1/c

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solvefor a, 1/a+1/b =c

solve for

a, \frac{1}{a} + \frac{1}{b} = c

a = - \frac{b}{1 - b c}; b \neq = \frac{1}{c}

Solution steps

\frac{1}{a} + \frac{1}{b} = c

Multiply by LCM

b + a = c ab

Move

b

to the right side

a = c ab - b

Move

c ab

to the left side

a - c ab = - b

Factor

a - c ab : a (1 - b c)

a (1 - b c) = - b

Divide both sides by

1 - b c; b \neq = \frac{1}{c}

a = - \frac{b}{1 - b c}; b \neq = \frac{1}{c}

\frac{5 x + 1}{x + 2} + \frac{x - 1}{x} = 2

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

- 6 - \frac{2}{x} = - 8 x

\frac{3 x + 1}{6 x - 2} = \frac{2 x + 5}{4 x - 13}

- \frac{3}{x ^{2} + 3 x} + 6 = \frac{1}{x + 3}

What is the answer to solvefor a, 1/a+1/b =c ?
The answer to solvefor a, 1/a+1/b =c is a=-b/(1-bc);\quad b\ne 1/c