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

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

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1/x =c+1/b

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

x = \frac{b}{c b + 1}; b \neq = 0, c \neq = - \frac{1}{b}

Solution steps

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

Multiply both sides by

x

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

Switch sides

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

Multiply both sides by

b

c x b + x = b; b \neq = 0

Factor

c x b + x : x (c b + 1)

x (c b + 1) = b; b \neq = 0

Divide both sides by

c b + 1; b \neq = 0, c \neq = - \frac{1}{b}

x = \frac{b}{c b + 1}; b \neq = 0, c \neq = - \frac{1}{b}

\frac{( x - 184 )}{x} \cdot 100 = 40

\frac{5}{x + 4} = 4 + \frac{7}{x - 2}

\frac{3 y}{y - 3} = 2 + \frac{9}{y - 3}

\frac{5}{x - 10} + \frac{5}{x} = 3

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

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