![]() ![]() Since this is true for all values of □, we can eliminate one of our variables □ or □ by substituting specific values of □. We represent this by using an equivalent sign. However, this equation should be true for all values of □. So we have □ is equal to □ times □ plus one plus □ times □ minus one. And canceling the shared factors in our numerator and our denominator on the right-hand side leaves us with □ times □ plus one plus □ times □ minus one. Canceling the shared factors in our numerator and our denominator on the left-hand side leaves us with □. Multiplying through by □ minus one times □ plus one gives us the following equation. To find the values of □ and □, we’re going to multiply both sides of our equation by □ minus one times □ plus one. Since we now have two unique factors in our denominator, by using partial fractions, we can rewrite □ of □ as □ divided by □ minus one plus □ divided by □ plus one for some constants □ and □. So we can factor this to give us □ minus one multiplied by □ plus one. We see that the denominator □ squared minus one is a difference between squares. To use partial fractions, we first need to fully factor the denominator of our rational function □ of □. It wants us to find the power series of this rational function by using partial fractions. The question gives us the rational function □ of □. Using partial fractions, calculate the power series of the function □ of □ is equal to □ divided by □ squared minus one. ![]()
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