Simplify: [(x2 - 2x - 3)/x2 - x - 2)]/[(x2 - 4x + 3)/(x2 + 5x - 6)]?

Answer 1

I'll assume you forget a bracket before the second x².

[(x² - 2x - 3)/(x² - x - 2)]/[(x² - 4x + 3)/(x² + 5x - 6)]

There are many ways to solve this. Since all of the quadratics are factorable, I'll do it that way.

x² - 2x - 3 factors to (x+1)(x-3). x² - x - 2 factors to (x+1)(x-2). x+1 divides out, and you're left with (x-3)/(x-2).

x² - 4x + 3 factors to (x-1)(x+6). x² + 5x - 6 factors to (x-1)(x+6). x-1 divides out, and you're left with (x-3)/(x+6).

Now, the problem is simplified to [(x-3)/(x-2)]/[(x-3)/(x+6)]. Since division is the same as multiplication by the reciprocal, we'll rewrite this as [(x-3)/(x-2)]*[(x+6)/(x-3)], or [(x-3)(x+6)]/[(x-2)(x-3)]. x-3 divides out, and we're left with our final answer of (x+6)/(x-2).

Answer 2

[(x2 - 2x - 3)/x2 - x - 2)]/[(x2 - 4x + 3)/(x2 + 5x - 6)] =
[(-x^3 - x^2 -2x -3)/x^2]/[(x - 3)/x + 6)] =
-(x + 6)(x^3 + x^2 + 2x + 3)/[x^2(x-3)]

[(x-3)(x+1)/(x-2)(x+1)]/[(x - 3)/x + 6)] =
[(x-3)/(x-2)]/[(x - 3)/x + 6)] =
(x+6)/(x-2)

Answer 3

((x^2 - 2x - 3)/(x^2 - x - 2)) / ((x^2 - 4x + 3)/(x^2 + 5x - 6))

((x^2 - 2x - 3)/(x^2 - x - 2)) * ((x^2 + 5x - 6)/(x^2 - 4x + 3))

((x^2 - 2x - 3)(x^2 + 5x - 6))/((x^2 - x - 2)(x^2 - 4x + 3))

((x - 3)(x + 1)(x + 6)(x - 1))/((x - 2)(x + 1)(x - 3)(x - 1))

The (x - 3)(x + 1)(x - 1) cancel out

ANS : (x + 6)/(x - 2)

Answer 4

the answer is (x+6)/(x-2)

Answer 5

52 and1/2?