When we add or subtract two fractions, they must have the same denominator.
We can multiply a complete equation by a lowest common denominator to "get rid of" all denominators, making the equation easier to solve.
Simplify the following equation to one that is quadratic:
|x - 1||x + 2|
We multiply the whole equation by (x - 1) (x + 2).
This gives us:
2 (x + 2) + 3 (x - 1) = 4 (x - 1) (x + 2)
Simplify to get:
2x + 4 + 3x - 3 = 4 (x2 + x - 2)
5x + 1 = 4x2 + 4x - 8
4x2 + 4x - 8 - 5x - 1 = 0
4x2 - x - 9 = 0
This can now be solved using the quadratic formula, but for this worksheet we just need to arrive at this quadratic equation in the form ax2 + bx + c = 0