Question

Find the simplified quotient. (2x^2 + 5x +3 / x^2 - 3x -4) / (4x^2 + 2x - 6 / x^2 - 8x + 16)

Answer 1

ANSWER

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

EXPLANATION

The given expression is;

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

We factor to obtain;

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

Multiply by the reciprocal of the second fraction

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

Cancel out common factors to get,

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

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

Answer 2

Answer:

X-4/2x-2

Step-by-step explanation: