Solve for D H=b/(D+d)

$H = \frac{b}{D + d}$

Step 1

Rewrite the equation as $\frac{b}{D + d} = H$ .

$\frac{b}{D + d} = H$

Step 2

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$D + d, 1$

Remove parentheses.

$D + d, 1$

The LCM of one and any expression is the expression.

$D + d$

Step 3

Multiply each term in $\frac{b}{D + d} = H$ by $D + d$ to eliminate the fractions.

Multiply each term in $\frac{b}{D + d} = H$ by $D + d$ .

$\frac{b}{D + d} (D + d) = H (D + d)$

Simplify the left side.

Cancel the common factor of $D + d$ .

Cancel the common factor.

$\frac{b}{D + d} (D + d) = H (D + d)$

Rewrite the expression.

$b = H (D + d)$

Simplify the right side.

Apply the distributive property.

$b = H D + H d$

Step 4

Solve the equation.

Rewrite the equation as $H D + H d = b$ .

$H D + H d = b$

Subtract $H d$ from both sides of the equation.

$H D = b - H d$

Divide each term in $H D = b - H d$ by $H$ and simplify.

Divide each term in $H D = b - H d$ by $H$ .

$\frac{H D}{H} = \frac{b}{H} + \frac{- H d}{H}$

Simplify the left side.

Cancel the common factor of $H$ .

Cancel the common factor.

$\frac{H D}{H} = \frac{b}{H} + \frac{- H d}{H}$

Divide $D$ by $1$ .

$D = \frac{b}{H} + \frac{- H d}{H}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $H$ .

Cancel the common factor.

$D = \frac{b}{H} + \frac{- H d}{H}$

Divide $- 1 d$ by $1$ .

$D = \frac{b}{H} - 1 d$

Rewrite $- 1 d$ as $- d$ .

$D = \frac{b}{H} - d$

Solve for D H=b/(D+d)

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