Chapter A.5, Problem 41AYU

To determine

To find: Simplify the given in factored form.

Answer to Problem 41AYU

$-\frac{\left(x+3\right)\left(3x-1\right)}{{\left(x^2+1\right)}^2}$

Explanation of Solution

Given:

$\frac{\left(x^2+1\right).3-\left(3x+4\right).2x}{{\left(x^2+1\right)}^2}$

Calculation:

$\frac{\left(x^2+1\right).3-\left(3x+4\right).2x}{{\left(x^2+1\right)}^2}=\frac{\left(3x^2+3\right)-\left(6x^2+8x\right)}{{\left(x^2+1\right)}^2}=\frac{-3x^2-8x+3}{{\left(x^2+1\right)}^2}=-\frac{\left(x+3\right)\left(3x-1\right)}{{\left(x^2+1\right)}^2}$