Step 1: Trying to factor as a Difference of Squares:
Factoring: x²⁰⁰² - 1
Theory : A difference of two perfect squares, A² - B² can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A² - AB + BA - B² =
A² - AB + AB - B²
A² - B²
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 1 is the square of 1
Check: x²⁰⁰² is the square of x¹⁰⁰¹
Factorization is : (x¹⁰⁰¹ + 1) × (x¹⁰⁰¹ - 1)
Answer:
-1 / x + (x + 1) / (x² + 3)
Step-by-step explanation:
(x − 3) / (x (x² + 3))
There are two factors in the denominator, so split this into two fractions with unknown numerators:
A / x + (Bx + C) / (x² + 3)
Combine back into one fraction:
(A (x² + 3) + (Bx + C) x) / (x (x² + 3))
Now equate this numerator with the original:
A (x² + 3) + (Bx + C) x = x − 3
Ax² + 3A + Bx² + Cx = x − 3
(A + B) x² + Cx + 3A = x − 3
Match the coefficients:
A + B = 0
C = 1
3A = -3
Solve:
A = -1
B = 1
C = 1
Therefore, the partial fraction decomposition is:
-1 / x + (x + 1) / (x² + 3)
Here's a graph showing that the two are the same:
desmos.com/calculator/hrxfnijewh
Answer:
1,224,780
Step-by-step explanation:
44,700 × 27.4= 1,224,780
Answer:
C.
Step-by-step explanation:
its C.
