474/VB01. problem / Math - Solved Math Problems

MR-474 / 894b. problem

Simplify the fraction below::

$\frac{a^{4} + 1 - 2 a^{2}}{1 - a - a^{2} + a^{3}}$

$\frac{a^{4} + 1 - 2 a^{2}}{1 - a - a^{2} + a^{3}} =$

$\frac{a^{4} - 2 a^{2} + 1}{a^{3} - a^{2} - a + 1}$

$= \frac{{(a^{2} - 1)}^{2}}{a^{2} (a - 1) - 1 (a - 1)}$

$= \frac{{(a^{2} - 1)}^{2}}{(a - 1) \cdot (a^{2} - 1)}$

$= \frac{{(a^{2} - 1)}^{2}}{(a - 1) \cdot (a - 1) (a + 1)}$

$= \frac{{(a^{2} - 1)}^{2}}{(a - 1) \cdot (a + 1) (a - 1)}$

$= \frac{{(a^{2} - 1)}^{2}}{(a^{2} - 1) (a - 1)}$

$= \frac{(a^{2} - 1) \cdot (a^{2} - 1)}{(a^{2} - 1) (a - 1)}$

$= \frac{(a^{2} - 1)}{(a - 1)}$

$= \frac{(a - 1) \cdot (a + 1)}{(a - 1)}$

$= a + 1$

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