Question

write the rational expression in lowest terms.
$\frac{15x^{2}+60x}{5x^{2}}$
what is the expression in lowest terms?

Explanation:

Step1: Factor the numerator

Factor out the greatest - common factor from \(15x^{2}+60x\). The GCF of \(15x^{2}\) and \(60x\) is \(15x\), so \(15x^{2}+60x = 15x(x + 4)\).
The rational expression becomes \(\frac{15x(x + 4)}{5x^{2}}\).

Step2: Simplify the coefficients and variables

Simplify the coefficient \(\frac{15}{5}=3\), and simplify the variable part \(\frac{x}{x^{2}}=\frac{1}{x}\) (using the rule \(\frac{a^{m}}{a^{n}}=a^{m - n}\), here \(m = 1\) and \(n = 2\)).
So \(\frac{15x(x + 4)}{5x^{2}}=\frac{3(x + 4)}{x}=\frac{3x+12}{x}\).

Answer:

\(\frac{3x + 12}{x}\)