Answer:
Option (1)
Step-by-step explanation:
The given expression in the figure attached is,
[tex]\frac{(2x+5)}{3x}[/tex] ÷ [tex]\frac{(2x-1)}{(2x+1)}[/tex]
We further simplify this expression,
[tex]\frac{(2x+5)}{3x}[/tex] ÷ [tex]\frac{(2x-1)}{(2x+1)}[/tex]
= [tex]\frac{(2x+5)}{3x}\times \frac{(2x+1)}{(2x-1)}[/tex]
= [tex]\frac{2x(2x+1)+5(2x+1)}{3x(2x-1)}[/tex] [By distributive property]
= [tex]\frac{4x^2+2x+10x+5}{6x^{2}-3x}[/tex]
= [tex]\frac{4x^2+12x+5}{6x^2-3x}[/tex]
Therefore, Option (1) will be the answer.
