Question

Find the quotient write your answer in the simplest form !

Answer 1

Second choice

Explanation:

If we factor all the numerators and denominators we get

(2x - 3)(2x + 3) (2x - 1)(2x + 1)

-------------------- ÷ -----------------

(2x + 3)(3x + 2) (3x + 2)(2x - 1)

2x - 3 3x + 2

= -------- * --------- = 2x - 3 / 2x + 1 (answer) (second choice)

3x + 2 2x + 1

Answer 2

The answer is B)
`(2x-3)/(2x+1)`

Explanation:

Step 1: First we have to factorize the each rational expressions.

`(4x^2 - 9)/(6x^2 + 13x + 6)` ÷
`(4x^2 - 1)/(6x^2 + x -2)`

=
`((2x - 3)(2x + 3))/((3x + 2)(2x + 3))`÷
`((2x+1)(2x -1))/((2x -1)(3x +2))`

Now we can cancel out (2x + 3) and (2x -1) since they are common factor both in the numerator and the denominator, so we get

=
`(2x - 3)/(3x + 2)` ÷
`(2x + 1)/(3x + 2)`

Step 2: If we have fraction over fraction, we can flip the second fraction and multiply.

=
`(2x - 3)/(3x + 2)` x
`(3x + 2)/(2x + 1)`

Now we can cancel out (3x + 2), so we get

=
`(2x-3)/(2x+1)`

Thefore, the answer is B.

Thank you.