Answer: [tex]\frac{x-4}{2x-2}[/tex]
Step-by-step explanation:
[tex]\frac{2x^2+5x+3}{x^2-3x-4}[/tex] divided by [tex]\frac{4x^2+2x-6}{x^2-8x+16}[/tex] is the same thing as multiplying [tex]\frac{2x^2+5x+3}{x^2-3x-4}[/tex] by [tex]\frac{x^2-8x+16}{4x^2+2x-6}[/tex].
The equation we get is:
[tex]\frac{2x^2+5x+3}{x^2-3x-4}*\frac{x^2-8x+16}{4x^2+2x-6}[/tex]
With this equation, we can factor each equation:
[tex]\frac{(x+1)(2x+3)}{(x+1)(x-4)} *\frac{(x-4)(x-4)}{2(x-1)(2x+3)}[/tex]
We can cancel out like terms since they would be dividing each other:
[tex]\frac{x-4}{2x-2}[/tex]
