Question

Simplify completely (6x² - 54x + 84 / 8x² -40 x +48) ÷ (x² + x - 56 / 2x² + 12x -32)

Answer 1

Answer:

The answer to your question is     $\frac{3(x - 2)}{2(x - 3)}$ or $\frac{3x - 6}{2x - 6}$

Step-by-step explanation:

Expression $\frac{6x^{2}- 54x + 84}{8x^{2} - 40x + 48} / \frac{ x^{2} + x - 56}{2x^{2} + 12x - 32}$

Process

1.- Change the division to a multiplication

                   $\frac{6x^{2}- 54x + 84}{8x^{2} - 40x + 48} x \frac{2x^{2}+ 12x - 32}{x^{2} + x - 56}$

2.- Factor

                   $\frac{6(x^{2}- 9x - 14)}{8(x^{2} - 5x + 6)} x \frac{2(x^{2}+ 6x - 16)}{(x^{2} + x -56)}$

                   $\frac{6(x + 8)(x - 2)}{8(x - 3)(x - 2)} x \frac{2(x + 8)(x - 2)}{(x + 8)(x - 7)}$

3.- Simplify (cancel the terms that are repeated in both numerator and denominator)

                  $\frac{2(6)(x - 2)}{8(x - 3)}$

                  $\frac{3(x - 2)}{2(x - 3)}$ or $\frac{3x - 6}{2x - 6}$