Answer:
The correct option is 1.
Step-by-step explanation:
The given expression is
[tex]\frac{2x^2+5x+3}{x^2-3x-4}\div \frac{4x^2+2x-6}{x^2-8x+16}[/tex]
Factories numerator and denominator.
[tex]\frac{2x^2+2x+3x+3}{x^2-4x+x-4}\div \frac{4x^2+6x-4x-6}{x^2-4x-4x+16}[/tex]
[tex]\frac{2x(x+1)+3(x+1)}{x(x-4)+(x-4)}\div \frac{2x(2x+3)-2(2x+3)}{x(x-4)-4(x-4)}[/tex]
[tex]\frac{(x+1)(2x+3)}{(x-4)(x+1)}\times \frac{(x-4)(x-4)}{(2x+3)(2x-2)}[/tex]
Cancel out the common factors.
[tex]\frac{1}{1}\times \frac{(x-4)}{(2x-2)}[/tex]
[tex]\frac{x-4}{2x-2}[/tex]
Therefore the correct option is 1.
