Simplify : 1/(a + 1) - a/(a ^ 2 - 1) - (a ^ 2)/(1 - a ^ 4) .
You asked:
Simplify the expression: \(\frac{1}{a + 1} - \frac{a}{{a}^{2} - 1} - \frac{{a}^{2}}{1 - {a}^{4}}\)
MathBot Answer:
Simplified:
\[ \frac{1}{a + 1} - \frac{a}{{a}^{2} - 1} - \frac{{a}^{2}}{1 - {a}^{4}} = - \frac{1}{a^{4} - 1} \]
Expanded:
\[ \frac{1}{a + 1} - \frac{a}{{a}^{2} - 1} - \frac{{a}^{2}}{1 - {a}^{4}} = - \frac{a^{2}}{1 - a^{4}} - \frac{a}{a^{2} - 1} + \frac{1}{a + 1} \]
Factored:
\[ \frac{1}{a + 1} - \frac{a}{{a}^{2} - 1} - \frac{{a}^{2}}{1 - {a}^{4}} = - \frac{1}{\left(a^{2} + 1\right) \left(a - 1\right) \left(a + 1\right)} \]