Answer:
2x-3
______
8x³•(x-3)
Explanation:
LET ME EXPLAIN, THAT HOW I GET THE ANSWER
STEP 1
((4•(x2))-9)
———————————————— ÷ (2x+3) ÷ (22x2-12x)
(((2•(x2))-9)+9)
STEP 2
((4•(x2))-9)
———————————— ÷ (2x+3) ÷ (4x2-12x)
((2x2-9)+9)
STEP 3
(22x2 - 9)
—————————— ÷ (2x + 3) ÷ (4x2 - 12x)
2x2
STEP 4
4x2 - 9
Simplify ———————
2x2
MY EXPLANATION THAT HOW TO GET THE SQUARE:
Trying to factor as a Difference of Squares:
4.1 Factoring: 4x2 - 9
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 : 4 is the square of 2
Check : 9 is the square of 3
Check : x2 is the square of x1
Factorization is : (2x + 3) • (2x - 3)
4.2 Attempting Polynomial Long Division
Attempted Long division of
2x + 3
By :
2x2
Was aborted due to the followinf reason :
Divisor bigger than Dividend
THIS IS THE CONTINUATION OF MY ANSWER:
Equation at the end of step 4
(2x + 3) • (2x - 3)
——————————————————— ÷ (2x + 3) ÷ (4x2 - 12x)
2x2
STEP 5
(2x+3)•(2x-3)
Divide ————————————— by 2x+3
2x2
Canceling Out :
5.1 Cancel out (2x + 3) which appears on both sides of the fraction line.
Equation at the end of step 5
(2x - 3)
———————— ÷ (4x2 - 12x)
2x2
STEP 6
2x-3
Divide ———— by 4x2-12x
2x2
STEP 7
Pulling out like terms
7.1 Pull out like factors :
4x2 - 12x = 4x • (x - 3)
Multiplying exponential expressions :
7.2 x2 multiplied by x1 = x(2 + 1) = x3
This is the final ans:
2x - 3
—————————————
8x3 • (x - 3)