Answer:
Option A is correct
\(\frac{2x^2+49}{x(x-7)}\)
Step-by-step explanation:
Given that:
\(\frac{3x}{x-7}-\frac{x+7}{x}\)
Take LCM of (x-7) and x is, x(x-7)
then;
\(\frac{3x(x)-(x+7)(x-7)}{x(x-7)}\)
Using identity rule:
\((a+b)(a-b)=a^2-b^2\)
⇒\(\frac{3x^2-(x^2-7^2)}{x(x-7)}\)
⇒\(\frac{3x^2-(x^2-49)}{x(x-7)}\)
Remove the bracket
⇒\(\frac{3x^2-x^2+49}{x(x-7)}\)
Combine like terms:
⇒\(\frac{2x^2+49}{x(x-7)}\)
Therefore, \(\frac{2x^2+49}{x(x-7)}\) is equivalent to \(\frac{3x}{x-7}-\frac{x+7}{x}\)
