Solve for b 1/a=bc+1/d

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

Rewrite the equation as $b c + \frac{1}{d} = \frac{1}{a}$ .

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

Subtract $\frac{1}{a}$ from both sides of the equation.

$b c + \frac{1}{d} - \frac{1}{a} = 0$

Move all terms not containing $b$ to the right side of the equation.

Subtract $\frac{1}{d}$ from both sides of the equation.

$b c - \frac{1}{a} = - \frac{1}{d}$

Add $\frac{1}{a}$ to both sides of the equation.

$b c = - \frac{1}{d} + \frac{1}{a}$

Divide each term in $b c = - \frac{1}{d} + \frac{1}{a}$ by $c$ and simplify.

Divide each term in $b c = - \frac{1}{d} + \frac{1}{a}$ by $c$ .

$\frac{b c}{c} = \frac{- \frac{1}{d}}{c} + \frac{\frac{1}{a}}{c}$

Simplify the left side.

Cancel the common factor of $c$ .

Cancel the common factor.

$\frac{b c}{c} = \frac{- \frac{1}{d}}{c} + \frac{\frac{1}{a}}{c}$

Divide $b$ by $1$ .

$b = \frac{- \frac{1}{d}}{c} + \frac{\frac{1}{a}}{c}$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$b = - \frac{1}{d} \cdot \frac{1}{c} + \frac{\frac{1}{a}}{c}$

Multiply $\frac{1}{c}$ by $\frac{1}{d}$ .

$b = - \frac{1}{c d} + \frac{\frac{1}{a}}{c}$

Multiply the numerator by the reciprocal of the denominator.

$b = - \frac{1}{c d} + \frac{1}{a} \cdot \frac{1}{c}$

Multiply $\frac{1}{a}$ by $\frac{1}{c}$ .

$b = - \frac{1}{c d} + \frac{1}{a c}$