Question

How do you simplify `\frac { 3x ^ { 3} - 48x } { x + 4} \cdot \frac { 6x ^ { 2} - 600} { x ^ { 2} - 17x + 70} \div \frac { x ^ { 2} - 5x + 4} { x ^ { 2} - 8x + 7}`?

Answer 1

`=>(3x^3 - 48x)/(x + 4) * (6x^2 - 600)/(x^2 - 17x + 70) *(x^2 - 8x + 7)/(x^2 - 5x + 4)`

`=> (3x(x^2 - 16))/(x + 4) * (6(x^2 -100))/((x - 10)(x - 7)) * ((x - 7)(x - 1))/((x - 4)(x - 1))`

`=>((3x)(x + 4)(x - 4))/(x + 4) * (6(x + 10)(x - 10))/((x - 10)(x- 7)) * ((x- 7)(x- 1))/((x - 4)(x - 1))`

After eliminating the factors using the rule `a/a = 1, a!= 0`:

`=>18x(x + 10)`

Hopefully this helps!