Question

( 27ˣ + 9ˣ - 6 * 3ˣ ) / ( 3ˣ ( 3ˣ - 2 ))

Answer 1

$\frac{27^x+9^x-6*3^x}{3^x(3^x-2)} =\frac{3^x(9^x+3^x-6)}{3^x-2} =\frac{(3^x+3)(3^x-2)}{3^x-2} =3^x+3$

Answer 2

To simplify the expression (27ˣ + 9ˣ - 6 * 3ˣ) / (3ˣ * (3ˣ - 2)), we can factor out common terms in the numerator and then simplify the resulting expression.

Step 1: Factor out common terms in the numerator. Notice that 27ˣ = (3ˣ)³ and 9ˣ = (3ˣ)². So, we can rewrite the expression as follows:

(3ˣ)³ + (3ˣ)² - 6 * 3ˣ

Step 2: Simplify the expression in the numerator. Now we can combine the terms with the same base, which is 3ˣ:

(3ˣ)³ + (3ˣ)² - 6 * 3ˣ = 3ˣ(3ˣ² + 3ˣ - 6)

Step 3: Factor out common terms in the denominator. The denominator is 3ˣ * (3ˣ - 2). It is already in its simplest form.

Now the simplified expression is:

(3ˣ(3ˣ² + 3ˣ - 6)) / (3ˣ * (3ˣ - 2))

Step 4: Cancel out common terms. In this case, the 3ˣ term in the numerator and denominator can be canceled out:

(3ˣ(3ˣ² + 3ˣ - 6)) / (3ˣ * (3ˣ - 2)) = (3ˣ² + 3ˣ - 6) / (3ˣ - 2)

So, the simplified expression is (3ˣ² + 3ˣ - 6) / (3ˣ - 2).