Solve for b (a+1)b=a+1

$(a + 1) b = a + 1$

Divide each term in $(a + 1) b = a + 1$ by $a + 1$ .

$\frac{(a + 1) b}{a + 1} = \frac{a}{a + 1} + \frac{1}{a + 1}$

Simplify the left side.

Cancel the common factor of $a + 1$ .

Cancel the common factor.

$\frac{(a + 1) b}{a + 1} = \frac{a}{a + 1} + \frac{1}{a + 1}$

Divide $b$ by $1$ .

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

Simplify the right side.

Combine the numerators over the common denominator.

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

Cancel the common factor of $a + 1$ .

Cancel the common factor.

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

Rewrite the expression.

$b = 1$