Question

Find the LCD of \(\frac{-2}{x+9}\) and \(\frac{5 x}{x^{2}+9 x}\) (A) \(\frac{x-1}{(x-1)(2 x+1)}\) \((\mathbf{B})-\frac{x}{x-1}\) (c) \(\frac{2 x^{2}+1}{(x-1)(2 x+1)}\) (D) \(\frac{2 x^{2}-1}{(x-1)(2 x+1)}\)

Short answer

None of the given options corresponds to the LCD of the given fractions

Step-by-step solution

Identify the Denominators

The denominators of the two fractions are \(x + 9\) and \(x^2 + 9x\). For the second denominator, factor out the common term to get \(x(x+9)\).

Find the LCD

The LCD is the expression that includes all individual factors of the denominators. Since the denominators share the same factors of \(x\) and \(x+9\), the LCD is actually \(x(x+9)\).

Compare with Choices

We find that none of the options matches the LCD derived from the given fractions. The problem seems to be misstated or it could be that we are given incorrect options.