Solve the Rational Equation for x 3^(x+1)+3^x=12

$3^{x + 1} + 3^{x} = 12$

Step 1

Factor out $3^{x}$ from the expression.

$3^{x} (3 + 1)$

Step 2

Add $3$ and $1$ .

$3^{x} \cdot 4 = 12$

Step 3

Move $4$ to the left of $3^{x}$ .

$4 \cdot 3^{x} = 12$

Step 4

Divide each term in $(4 \cdot 3^{x}) = 12$ by $4$ and simplify.

Divide each term in $(4 \cdot 3^{x}) = 12$ by $4$ .

$\frac{(4 \cdot 3^{x})}{4} = \frac{12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 \cdot 3^{x}}{4} = \frac{12}{4}$

Divide $3^{x}$ by $1$ .

$3^{x} = \frac{12}{4}$

Simplify the right side.

Divide $12$ by $4$ .

$3^{x} = 3$

Step 5

Create equivalent expressions in the equation that all have equal bases.

$3^{x} = 3^{1}$

Step 6

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x = 1$