Solve for d (b+4)/(c+d)=a

$\frac{b + 4}{c + d} = a$

Step 1

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.

$c + d, 1$

Remove parentheses.

$c + d, 1$

The LCM of one and any expression is the expression.

$c + d$

Step 2

Multiply each term in $\frac{b + 4}{c + d} = a$ by $c + d$ to eliminate the fractions.

Multiply each term in $\frac{b + 4}{c + d} = a$ by $c + d$ .

$\frac{b + 4}{c + d} (c + d) = a (c + d)$

Simplify the left side.

Cancel the common factor of $c + d$ .

Cancel the common factor.

$\frac{b + 4}{c + d} (c + d) = a (c + d)$

Rewrite the expression.

$b + 4 = a (c + d)$

Simplify the right side.

Apply the distributive property.

$b + 4 = a c + a d$

Step 3

Solve the equation.

Rewrite the equation as $a c + a d = b + 4$ .

$a c + a d = b + 4$

Subtract $a c$ from both sides of the equation.

$a d = b + 4 - a c$

Divide each term in $a d = b + 4 - a c$ by $a$ and simplify.

Divide each term in $a d = b + 4 - a c$ by $a$ .

$\frac{a d}{a} = \frac{b}{a} + \frac{4}{a} + \frac{- a c}{a}$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a d}{a} = \frac{b}{a} + \frac{4}{a} + \frac{- a c}{a}$

Divide $d$ by $1$ .

$d = \frac{b}{a} + \frac{4}{a} + \frac{- a c}{a}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $a$ .

Cancel the common factor.

$d = \frac{b}{a} + \frac{4}{a} + \frac{- a c}{a}$

Divide $- 1 c$ by $1$ .

$d = \frac{b}{a} + \frac{4}{a} - 1 c$

Rewrite $- 1 c$ as $- c$ .

$d = \frac{b}{a} + \frac{4}{a} - c$

Solve for d (b+4)/(c+d)=a

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