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Find the quotient write your answer in the simplest form !

Find the quotient write your answer in the simplest form !-example-1

2 Answers

3 votes

Answer:

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

User Apgsov
by
8.2k points
2 votes

Answer:

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.

User Schaz
by
8.1k points

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