Simplify the following expression: $$ \frac{3 x+x^{2}}{18+6 x} $$

Question

UpStudy AI · Accepted Answer

We start with the expression:
$$
\frac{3x + x^2}{18 + 6x}
$$

**Step 1: Factor the numerator**

The numerator $$3x + x^2$$ can be factored by taking out the common factor $$x$$:
$$
3x + x^2 = x(3 + x)
$$

**Step 2: Factor the denominator**

The denominator $$18 + 6x$$ can be factored by taking out the common factor $$6$$:
$$
18 + 6x = 6(3 + x)
$$

**Step 3: Write the expression with the factored forms**

Substitute the factorizations back into the expression:
$$
\frac{x(3 + x)}{6(3 + x)}
$$

**Step 4: Cancel common factors**

Notice that $$(3 + x)$$ is a common factor in both the numerator and the denominator. Cancel it, assuming $$3 + x \neq 0$$:
$$
\frac{x \cancel{(3 + x)}}{6 \cancel{(3 + x)}} = \frac{x}{6}
$$

**Final Answer:**

$$
\frac{x}{6}
$$
The simplified expression is $$ \frac{x}{6} $$.

Simplify the following expression:

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions