Question

How do you simplify `(x^2 +3x)/(2x-14)*(x^2 -49)/(x^2 – 2x -15)`#?

Answer 1

`(x(x-7))/(2(x-5))=(x²-7x)/(2x-10)`

Explanation:

[0] `(x²+3x)/(2x-14)*(x²-49) /(x²-2x-15)` first let's multiply.
[1]`((x²+3x)(x²-49)) /((2x-14)(x²-2x-15))`, then,
`a²-b²=(a-b) (a+b)`
[2]`(x(x+3)(x-7)cancel(x+7))/(2(cancel(x+7)) (x²-2x-15))` now, we see that `color(red)(-3 and 5)` are trivial roots of `(x²-2x-15)`
[3] `(x(cancel(x+3))(x-7))/(2(cancel(x+3))(x-5))`
[4]`(x(x-7))/(2(x-5))`
[5]`(x²-7x)/(2x-10)`