Question

How do you simplify `\frac { x ^ { 2} - x - 6} { x ^ { 2} + 2x } \cdot \frac { x ^ { 3} + x ^ { 2} } { x ^ { 2} - 2x - 3}`?

Answer 1

The expression simplifies to `x`.

Explanation:

`frac{x^2-x-6}{x^2-2x} * frac{x^3+x^2}{x^2-2x-3}`

Factor each numerator and denominator.

`frac{(x-3)(x+2)}{x(x+2)}*frac{x^2(x+1)}{(x-3)(x+1)}`

Cancel any factors that are the same in numerator and denominator.

`frac{color(red)(cancel((x-3)))color(blue)(cancel((x+2)))}{xcolor(blue)(cancel((x+2)))}*frac{x^2cancel((x+1))}{color(red)(cancel((x-3)))cancel((x+1))}`

`x^2/xcolor(white)(aaa)`Use the exponent rule `x^a/x^b=x^(a-b)`

`x`