(4x^2-9)/(2x^2-9x+9) / (2x+3)/(4x^2-12x)

2x-3

8x³•(x-3)

Step-by-step 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)

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