If (frac{1}{p}) = (frac{a^2 + 2ab + b^2}{a – b}) and (frac{1}{q}) = (frac{a + b}{a^2 – 2ab + b^2}) Find (frac{p}{q})
-
A.
(frac{a + b}{a – b}) -
B.
(frac{1}{a^2 – b^2}) -
C.
(frac{a – b}{a + b}) -
D.
a2 – b2
Correct Answer: Option B
Explanation
(frac{1}{p} = frac{a^{2} + 2ab + b^{2}}{a – b})
(frac{1}{q} = frac{a + b}{a^{2} – 2ab + b^{2}})
(frac{1}{p} = frac{(a + b)^{2}}{a – b})
(frac{1}{q} = frac{a + b}{(a – b)^{2}})
(therefore p = frac{a – b}{(a + b)^{2}})
(frac{p}{q} = p times frac{1}{q} = frac{a – b}{(a + b)^{2}} times frac{a + b}{(a – b)^{2}})
= (frac{1}{(a + b)(a – b)})
= (frac{1}{a^{2} – b^{2}})