Solve for x a/(x+a)=b

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

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.

$x + a, 1$

Remove parentheses.

$x + a, 1$

The LCM of one and any expression is the expression.

$x + a$

Step 2

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

Multiply each term in $\frac{a}{x + a} = b$ by $x + a$ .

$\frac{a}{x + a} (x + a) = b (x + a)$

Simplify the left side.

Cancel the common factor of $x + a$ .

Cancel the common factor.

$\frac{a}{x + a} (x + a) = b (x + a)$

Rewrite the expression.

$a = b (x + a)$

Simplify the right side.

Apply the distributive property.

$a = b x + b a$

Step 3

Solve the equation.

Rewrite the equation as $b x + b a = a$ .

$b x + b a = a$

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

$b x = a - b a$

Divide each term in $b x = a - b a$ by $b$ and simplify.

Divide each term in $b x = a - b a$ by $b$ .

$\frac{b x}{b} = \frac{a}{b} + \frac{- b a}{b}$

Simplify the left side.

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{b x}{b} = \frac{a}{b} + \frac{- b a}{b}$

Divide $x$ by $1$ .

$x = \frac{a}{b} + \frac{- b a}{b}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $b$ .

Cancel the common factor.

$x = \frac{a}{b} + \frac{- b a}{b}$

Divide $- 1 a$ by $1$ .

$x = \frac{a}{b} - 1 a$

Rewrite $- 1 a$ as $- a$ .

$x = \frac{a}{b} - a$

Solve for x a/(x+a)=b

Related Questions

Support LCMGCF.com by disabling your adblocker.