Simplify Simplify the expression (9x3+6x2)/(3x+2)

Question

Solvely Expert · Accepted Answer

Solution:

Simplification Process

Step 1: Extract the common factor

Identify and factor out the common term $3 x^{2}$ from the numerator $9 x^{3} + 6 x^{2}$ .

Step 1.1

Extract $3 x^{2}$ from $9 x^{3}$ . We get $\frac{3 x^{2} (3 x) + 6 x^{2}}{3 x + 2}$ .

Step 1.2

Extract $3 x^{2}$ from $6 x^{2}$ . We get $\frac{3 x^{2} (3 x) + 3 x^{2} (2)}{3 x + 2}$ .

Step 1.3

Combine the factored terms. We obtain $\frac{3 x^{2} (3 x + 2)}{3 x + 2}$ .

Step 2: Simplify by canceling common factors

Eliminate the common factor $(3 x + 2)$ from the numerator and denominator.

Step 2.1

Cancel out the common factor. We have $\frac{3 x^{2} (3 x + 2)}{3 x + 2}$ .

Step 2.2

Simplify to get the final result: $3 x^{2}$ .

Knowledge Notes:

To simplify a rational expression, we can follow these steps:

Factorization: Break down both the numerator and denominator into their simplest factors. This involves identifying common terms or patterns that can be factored out.
Common Factors: Look for common factors in the numerator and denominator. These are terms that appear in both and can be canceled out to simplify the expression.
Cancellation: After factoring, cancel out the common factors. This is based on the principle that a fraction can be reduced by dividing both the numerator and the denominator by the same non-zero number or expression.
Simplify: Once the common factors are canceled, rewrite the expression in its simplest form.

In the given problem, we used the distributive property to factor out $3 x^{2}$ from the numerator. The distributive property states that for any numbers or expressions $a$ , $b$ , and $c$ , the equation $a (b + c) = a b + a c$ holds true. After factoring, we noticed that the term $(3 x + 2)$ was present in both the numerator and the denominator, allowing us to cancel it out and simplify the expression to $3 x^{2}$ .

Simplify Simplify the expression (9x^3+6x^2)/(3x+2)

Answer