Answer:
The answer to your question is [tex]\frac{3(x - 2)}{2(x - 3)}[/tex] or [tex]\frac{3x - 6}{2x - 6}[/tex]
Step-by-step explanation:
Expression [tex]\frac{6x^{2}- 54x + 84}{8x^{2} - 40x + 48} / \frac{ x^{2} + x - 56}{2x^{2} + 12x - 32}[/tex]
Process
1.- Change the division to a multiplication
[tex]\frac{6x^{2}- 54x + 84}{8x^{2} - 40x + 48} x \frac{2x^{2}+ 12x - 32}{x^{2} + x - 56}[/tex]
2.- Factor
[tex]\frac{6(x^{2}- 9x - 14)}{8(x^{2} - 5x + 6)} x \frac{2(x^{2}+ 6x - 16)}{(x^{2} + x -56)}[/tex]
[tex]\frac{6(x + 8)(x - 2)}{8(x - 3)(x - 2)} x \frac{2(x + 8)(x - 2)}{(x + 8)(x - 7)}[/tex]
3.- Simplify (cancel the terms that are repeated in both numerator and denominator)
[tex]\frac{2(6)(x - 2)}{8(x - 3)}[/tex]
[tex]\frac{3(x - 2)}{2(x - 3)}[/tex] or [tex]\frac{3x - 6}{2x - 6}[/tex]
