What is the answer to 1/x = 1/a+1/b ?

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

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1/x = 1/a+1/b

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

x = \frac{ab}{b + a}; ab \neq = 0, a \neq = - b

Solution steps

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

Multiply both sides by

x

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

Switch sides

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

Multiply by LCM

b x + a x = ab; ab \neq = 0

Factor

b x + a x : x (b + a)

x (b + a) = ab; ab \neq = 0

Divide both sides by

b + a; ab \neq = 0, a \neq = - b

x = \frac{ab}{b + a}; ab \neq = 0, a \neq = - b

\frac{6}{- x} = \frac{x}{- 24}

x^{- 4} = 16

\frac{n ^{2}}{y ^{2}} + \frac{y ^{2}}{n ^{2}} = 223

x, \frac{2}{x} + \frac{3}{y} = 1

\frac{x}{( x ^{2} + 1 )} + \frac{( x ^{2} + 1 )}{x} = \frac{5}{2}

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