165k views
2 votes
Fully simplify the expression: (6x³+12x²-210x)/(x²-49) . (6x)/(2x³-50x) ÷ (x+7)/(x²-49)

1 Answer

2 votes

Final answer:

To simplify the given expression, we factor where possible and then cancel out common factors. After this process, the expression simplifies to (18)/(x²-7x).

Step-by-step explanation:

To fully simplify the expression (6x³+12x²-210x)/(x²-49) × (6x)/(2x³-50x) ÷ (x+7)/(x²-49), we should first factor the polynomials where possible and cancel out common factors. Notice that x² - 49 is a difference of squares which can be factored into (x+7)(x-7). Additionally, the numerator 6x³+12x²-210x can be factored out by 6x, resulting in 6x(x²+2x-35), and x²+2x-35 can further be factored into (x+7)(x-5). Expression simplification involves canceling out common factors in the numerator and the denominator.

The expression simplifies as follows:

  1. Factor where possible
  2. Cancel out common factors
  3. Simplify the remaining terms

After factoring, the expression becomes:

(6x(x+7)(x-5)/(x+7)(x-7)) × (6x)/(2x(x²-25)) ÷ (x+7)/(x+7)(x-7)

We can now simplify:

(6x(x-5)/(x-7)) × (3)/(x(x-5)) ÷ 1/(x-7)

And finally:

(18)/(x²-7x)

This is a simplified expression.

User Daniel Larsson
by
7.7k points