Solve for x ax+b^2=a^2-bx

$a x + b^{2} = a^{2} - b x$

Step 1

Add $b x$ to both sides of the equation.

$a x + b^{2} + b x = a^{2}$

Step 2

Subtract $b^{2}$ from both sides of the equation.

$a x + b x = a^{2} - b^{2}$

Step 3

Factor $x$ out of $a x + b x$ .

Factor $x$ out of $a x$ .

$x a + b x = a^{2} - b^{2}$

Factor $x$ out of $b x$ .

$x a + x b = a^{2} - b^{2}$

Factor $x$ out of $x a + x b$ .

$x (a + b) = a^{2} - b^{2}$

Step 4

Divide each term in $x (a + b) = a^{2} - b^{2}$ by $a + b$ and simplify.

Divide each term in $x (a + b) = a^{2} - b^{2}$ by $a + b$ .

$\frac{x (a + b)}{a + b} = \frac{a^{2}}{a + b} + \frac{- b^{2}}{a + b}$

Simplify the left side.

Cancel the common factor of $a + b$ .

Cancel the common factor.

$\frac{x (a + b)}{a + b} = \frac{a^{2}}{a + b} + \frac{- b^{2}}{a + b}$

Divide $x$ by $1$ .

$x = \frac{a^{2}}{a + b} + \frac{- b^{2}}{a + b}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{a^{2} - b^{2}}{a + b}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

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

Cancel the common factor of $a + b$ .

Cancel the common factor.

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

Divide $a - b$ by $1$ .

$x = a - b$