Question

Find the simplified quotient.

Answer 1

The middle one..............

Answer 2

Answer:

The correct option is 1.

Step-by-step explanation:

The given expression is

$\frac{2x^2+5x+3}{x^2-3x-4}\div \frac{4x^2+2x-6}{x^2-8x+16}$

Factories numerator and denominator.

$\frac{2x^2+2x+3x+3}{x^2-4x+x-4}\div \frac{4x^2+6x-4x-6}{x^2-4x-4x+16}$

$\frac{2x(x+1)+3(x+1)}{x(x-4)+(x-4)}\div \frac{2x(2x+3)-2(2x+3)}{x(x-4)-4(x-4)}$

$\frac{(x+1)(2x+3)}{(x-4)(x+1)}\times \frac{(x-4)(x-4)}{(2x+3)(2x-2)}$

Cancel out the common factors.

$\frac{1}{1}\times \frac{(x-4)}{(2x-2)}$

$\frac{x-4}{2x-2}$

Therefore the correct option is 1.