Question

subtract the following rational expressions. (1 point)\\(\frac{x}{2x + 5}-\frac{2x}{6x + 15}=\frac{\square}{\square}\\)

Explanation:

Step1: Factor the denominator

Factor \(6x + 15\) to get \(3(2x + 5)\). So the expression becomes \(\frac{x}{2x + 5}-\frac{2x}{3(2x + 5)}\).

Step2: Find a common denominator

The common denominator of \(2x + 5\) and \(3(2x + 5)\) is \(3(2x + 5)\). Rewrite the first fraction with the common denominator: \(\frac{x\times3}{3(2x + 5)}-\frac{2x}{3(2x + 5)}\).

Step3: Subtract the numerators

Subtract the numerators: \(\frac{3x-2x}{3(2x + 5)}\).

Step4: Simplify the numerator

Simplify the numerator: \(\frac{x}{3(2x + 5)}=\frac{x}{6x + 15}\).

Answer:

\(\frac{x}{6x + 15}\) (or in boxed form for numerator and denominator: \(\boxed{x}\) and \(\boxed{6x + 15}\))