Question

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

Answer 1

X-4/2x-2

Explanation:

Answer 2

`(x - 4)/(2x - 2)`

EXPLANATION

The given expression is;

`\frac{2 {x}^(2) + 5x + 3}{ {x}^(2) - 3x - 4} / \frac{4 {x}^(2) + 2x - 6}{ {x}^(2) - 8x + 16}`

We factor to obtain;

`((x + 1)(2x + 3))/((x - 4)(x + 1)) / (2(x - 1)(2x + 3))/((x - 4)(x - 4))`

Multiply by the reciprocal of the second fraction

`((x + 1)(2x + 3))/((x - 4)(x + 1)) * ((x - 4)(x - 4))/(2(x - 1)(2x + 3))`

Cancel out common factors to get,

`(1)/(1) * ((x - 4))/(2(x - 1))`

`(x - 4)/(2x - 2)`