Question

Divide (4xsquare-9)by(2x-3)​

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

STEP

2

:

4x2 - 9

Simplify ———————

2x - 3

Trying to factor as a Difference of Squares:

2.1 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)

Canceling Out :

2.2 Cancel out (2x - 3) which appears on both sides of the fraction line.

Final result :

2x + 3