Questions: (6y+12)/(5y+10)

Solution Steps

To simplify the rational expression \(\frac{6y + 12}{5y + 10}\), we need to factor both the numerator and the denominator and then cancel out any common factors.

1. Factor the numerator: \(6y + 12\) can be factored as \(6(y + 2)\).
2. Factor the denominator: \(5y + 10\) can be factored as \(5(y + 2)\).
3. Cancel the common factor \((y + 2)\) from both the numerator and the denominator.

We start with the rational expression:

\[ \frac{6y + 12}{5y + 10} \]

We can factor the numerator and the denominator:

• The numerator \(6y + 12\) can be factored as \(6(y + 2)\).
• The denominator \(5y + 10\) can be factored as \(5(y + 2)\).

Thus, we rewrite the expression as:

\[ \frac{6(y + 2)}{5(y + 2)} \]

Next, we notice that \((y + 2)\) is a common factor in both the numerator and the denominator. We can cancel this common factor:

\[ \frac{6 \cancel{(y + 2)}}{5 \cancel{(y + 2)}} = \frac{6}{5} \]

Final Answer