Question

simplify.
\frac{14y + 49}{10y + 35}

Explanation:

Step1: Factor numerator and denominator

Factor out the greatest common factor (GCF) from the numerator \(14y + 49\) and the denominator \(10y + 35\). The GCF of \(14y\) and \(49\) is \(7\), so \(14y + 49 = 7(2y + 7)\). The GCF of \(10y\) and \(35\) is \(5\), so \(10y + 35 = 5(2y + 7)\).

$$ \frac{14y + 49}{10y + 35}=\frac{7(2y + 7)}{5(2y + 7)} $$

Step2: Cancel common factors

Since \(2y + 7\) is a common factor in the numerator and the denominator (and \(2y+7
eq0\), i.e., \(y
eq-\frac{7}{2}\)), we can cancel it out.

$$ \frac{7(2y + 7)}{5(2y + 7)}=\frac{7}{5} $$

Answer:

\(\frac{7}{5}\)