Final answer:
To find the value of A in the partial fraction expansion of -2x + 63 / ((x - 4)(x + 7)) = A / (x - 4) + B / (x + 7), we cleared the denominators and solved for A by setting x to 4, resulting in A = 5.
Step-by-step explanation:
The student has provided a partial fraction expansion problem, which is a concept in algebra where a complex fraction is broken down into simpler fractions that add up to the original fraction. To find the value of A in the partial fraction expansion of -2x + 63 / ((x - 4)(x + 7)) that is expressed as A / (x - 4) + B / (x + 7), we must clear the denominators and solve for A.
We begin by multiplying both sides of the equation by the common denominator (x - 4)(x + 7) to eliminate the fractions:
-2x + 63 = A(x + 7) + B(x - 4)
To solve for A, we can substitute x = 4 into the equation since this will cause the B term to drop out (because B(x - 4) will be zero when x = 4):
-2(4) + 63 = A(4 + 7)
-8 + 63 = A(11)
55 = A(11)
Divide both sides by 11 to get A:
A = 5
Therefore, the value of A in the given partial fraction expansion is 5.