QuestionAugust 25, 2025

(c^2-1)/(c^4)-1div (c+1)/(c^2)+1

(c^2-1)/(c^4)-1div (c+1)/(c^2)+1
(c^2-1)/(c^4)-1div (c+1)/(c^2)+1

Solution
4.5(193 votes)

Answer

\frac{1}{c-1} Explanation 1. Simplify the Division Rewrite the division as multiplication by the reciprocal: \frac{c^{2}-1}{c^{4}-1} \times \frac{c^{2}+1}{c+1}. 2. Factor Numerators and Denominators Factor c^{2}-1 = (c-1)(c+1) and c^{4}-1 = (c^{2}-1)(c^{2}+1) = (c-1)(c+1)(c^{2}+1). 3. Cancel Common Factors Cancel (c-1), (c+1), and (c^{2}+1) from numerator and denominator: \frac{(c-1)(c+1)}{(c-1)(c+1)(c^{2}+1)} \times \frac{c^{2}+1}{c+1} = \frac{1}{c-1}.

Explanation

1. Simplify the Division<br /> Rewrite the division as multiplication by the reciprocal: $\frac{c^{2}-1}{c^{4}-1} \times \frac{c^{2}+1}{c+1}$.<br /><br />2. Factor Numerators and Denominators<br /> Factor $c^{2}-1 = (c-1)(c+1)$ and $c^{4}-1 = (c^{2}-1)(c^{2}+1) = (c-1)(c+1)(c^{2}+1)$.<br /><br />3. Cancel Common Factors<br /> Cancel $(c-1)$, $(c+1)$, and $(c^{2}+1)$ from numerator and denominator: $\frac{(c-1)(c+1)}{(c-1)(c+1)(c^{2}+1)} \times \frac{c^{2}+1}{c+1} = \frac{1}{c-1}$.
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