Question

Which of the following is the quotient of the rational expressions shown below?

Answer 1

Option (1)

Explanation:

The given expression in the figure attached is,

`((2x+5))/(3x)` ÷
`((2x-1))/((2x+1))`

We further simplify this expression,

`((2x+5))/(3x)` ÷
`((2x-1))/((2x+1))`

=
`((2x+5))/(3x)* ((2x+1))/((2x-1))`

=
`(2x(2x+1)+5(2x+1))/(3x(2x-1))` [By distributive property]

=
`(4x^2+2x+10x+5)/(6x^(2)-3x)`

=
`(4x^2+12x+5)/(6x^2-3x)`

Therefore, Option (1) will be the answer.