write the partial fraction decomposition for the rational expression. Check your result algebraically by combining the fractions.
1/(x^2 -1)

Question

write the partial fraction decomposition for the rational expression. Check your result algebraically by combining the fractions.
1/(x^2 -1)

anonymous · Answer

$$ \large
\frac{1}{x^2-1}
$$First you factor it with difference of squares$$
\frac{1}{(x+1)(x-1)}
$$Now we want this form:$$
\frac{1}{(x+1)(x-1)} = \frac{A}{x+1}+\frac{B}{x-1}
$$We know that$$
A(x-1)+B(x+1)=1
$$Since it was used in order to get the numerator of 1.

anonymous · Answer

We get$$
Ax-A+Bx+B = 1
$$$$
(A+B)x+(B-A) = 1
$$

anonymous · Answer

So $$
(A+B)x+(B-A) = 0x+1
$$Gives us two equations:$$
A+B = 0\quad\quad B-A = 1
$$