Question

How do you simplify `\frac{x - 12}{3- x} = \frac{x + 8}{x + 12}`?

Answer 1

To simplify an equation, you want to combine all like terms. Start by (1.) cross multiplying and then (2.) combine all like terms. You would not need to factor because you are not asked to factor and because factoring does not simplify the equation any more than it is now.

1. `(x-12)(x+12)=(3-x)(x+8)`
2. `x^2-144=-x^2-5x+24` -> `2x^2+5x-168=0`

Answer 2

Apply the property `a/b = c/d -> a xx d = b xx c`.

`(x - 12)(x + 12) = (3 - x)(x + 8)`

`x^2 - 12x + 12x - 144 = 3x - x^2 - 8x + 24`

`2x^2 + 5x - 168 = 0`

I would recommend solving using the quadratic formula since the numbers are so large, and therefore it would be difficult to find factors.

`x = (-b +- sqrt(b^2 - 4ac))/(2a)`

`x = (-5 +- sqrt(5^2 - 4 xx 2 xx -168))/(2 xx 2)`

`x = 8, -21/2`

Hopefully this helps!