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}})
Correct Answer: Option B
Explanation
(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})