We must apply the partial fractions method in order to determine the partial fraction decomposition of 1 / (x^2 – 1).
It is possible to factor the denominator (x^2 – 1) as non-repeated linear factors (x – 1)(x + 1).
The following is the partial fraction decomposition of 1 / (x^2 – 1):
A / (x – 1) + B / (x + 1)
The following procedures can be used to determine the values of A and B:
Multiply the denominator (x^2 – 1) by both sides:
1 = A(x + 1) + B(x – 1)
Combining the constant term and the coefficients of x:
A + B = 0.
A minus B equals 1.
After the system of equations is solved, we obtain: A = 1/2 B = -1/2
Consequently, 1 / (x^2 – 1)’s partial fraction decomposition is:
1 / (x^2 – 1) = 1 / (2(x – 1)) + 1 / (2(x + 1))
We must apply the partial fractions method in order to determine the partial fraction decomposition of 1 / (x^2 – 1).
It is possible to factor the denominator (x^2 – 1) as non-repeated linear factors (x – 1)(x + 1).
The following is the partial fraction decomposition of 1 / (x^2 – 1):
A / (x – 1) + B / (x + 1)
The following procedures can be used to determine the values of A and B:
Multiply the denominator (x^2 – 1) by both sides:
1 = A(x + 1) + B(x – 1)
Combining the constant term and the coefficients of x:
A + B = 0.
A minus B equals 1.
After the system of equations is solved, we obtain: A = 1/2 B = -1/2
Consequently, 1 / (x^2 – 1)’s partial fraction decomposition is:
1 / (x^2 – 1) = 1 / (2(x – 1)) + 1 / (2(x + 1))
