Question

try it!
try: rewrite expressions with common denominators
celeste wants to find the sum of \\(\frac{3}{x}\\) and \\(\frac{x}{2x - 3}\\). in order to add the two rational expressions, she must first find a common denominator by operation the two denominators, \\(x\\) and \\(2x - 3\\).
next, she needs to rewrite each rational expression using the common denominator. the first term can be rewritten as \\(\frac{3(2x - 3)}{x(2x - 3)}\\), and the second term can be rewritten as .
check
explain

Explanation:

Step1: Identify common denominator

The denominators are \(x\) and \(2x - 3\). The common denominator is their product, \(x(2x - 3)\).

Step2: Rewrite the second term

To rewrite \(\frac{x}{2x - 3}\) with denominator \(x(2x - 3)\), multiply numerator and denominator by \(x\).

$$ \frac{x}{2x - 3} \times \frac{x}{x} = \frac{x \times x}{x(2x - 3)} = \frac{x^2}{x(2x - 3)} $$

Answer:

\(\frac{x^2}{x(2x - 3)}\)