Question

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

Answer 1

`-((x-1))/((x+1))`

Explanation:

Before you can simplify this fraction, you need to find factors of the two quadratic trinomials first.

`\frac {color(blue)( x ^ { 2} + 2x - 3)} { color(lime)(x ^ { 2} - 2x - 3)} xx \frac { 3- x } { 3+ x }`

`(color(blue)((x+3)(x-1)))/(color(lime)((x-3)(x+1))) xx color(red)((3-x))/(3+x)`

In `color(red)((3-x)` notice that of these signs were the other way around we would be able to cancel two factors, but `" "(3+x) = (x+3)`

We can change the signs around if we divide by `-1`

`color(red)((3-x) = -(x-3)`

`((x+3)(x-1))/((x-3)(x+1)) xx color(red)(-(x-3))/((x+3))`

Cancel any like factors as long as it is 'through' a X

`(cancel(x+3)(x-1))/(cancel(x-3)(x+1)) xx color(red)(-cancel(x-3))/(cancel(x+3))`

=`(-(x-1))/((x+1))`