Question

Find the quotient write your answer in the simplest form !

Answer 1

Answer:

The answer is B)  $\frac{2x-3}{2x+1}$

Step-by-step explanation:

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

$\frac{4x^2 - 9}{6x^2 + 13x + 6}$ ÷$\frac{4x^2 - 1}{6x^2 + x -2}$

= $\frac{(2x - 3)(2x + 3)}{(3x + 2)(2x + 3)}$÷$\frac{(2x+1)(2x -1)}{(2x -1)(3x +2)}$

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

= $\frac{2x - 3}{3x + 2}$ ÷$\frac{2x + 1}{3x + 2}$

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

= $\frac{2x - 3}{3x + 2}$ x $\frac{3x + 2}{2x + 1}$

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

= $\frac{2x-3}{2x+1}$

Thefore, the answer is B.

Thank you.

Answer 2

Answer:

Second choice

Step-by-step 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