Simplify \(\frac{a - b}{a + b}\) - \(\frac{a + b}{a - b}\)
A
\(\frac{4ab}{a - b}\)
B
\(\frac{-4ab}{a^2 - b^2}\)
C
\(\frac{-4ab}{a^{-2} - b}\)
D
\(\frac{4ab}{a^{-2} - b^{-2}}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{a - b}{a + b}\) - \(\frac{a + b}{a - b}\) = \(\frac{(a - b)^2}{(a + b)}\) - \(\frac{(a + b)^2}{(a - b0}\)
applying the principle of difference of two sqrt. Numerator = (a - b) + (a + b) (a - b) - (a + b)
= (a = b + a = b)(a = b - a = b)
2a(-2b) = -4ab
= \(\frac{-4ab}{(a + b)(a - b)}\)
= \(\frac{-4ab}{a^2 - b^2}\)
Source: Myschool Past Questions Archive (Record #32700)