Sometimes instead of leaving a rational expression in fraction form you want to perform the division. If the divisor is a monomial (like 3x) this process is simple,
just split the numerator into a sum of terms with each divided by the divisor. For example:
| 2x2 + 6x - 5 | = | 2x2 | + | 6x | + | -5 |
= x + 3 + | -5 |
| 2x | 2x | 2x | 2x | 2x |
When the divisor is itself a polynomial the matter isn't quite so simple, you'll need to use long division the same way you would with whole numbers. For example to divide
x2 + 2x + 4 by
x - 1:
| | x + 3 |
| x - 1 | x2 | + 2x | + 4 |
| | x2 | - x | |
| | | 3x | + 4 |
| | | 3x | - 3 |
| | | | 7 |
| The quotient would then be x + 3 + | 7 |
| x - 1 |
It is important to remember to subtract when you bring the value down, in the above example +2x - (-x) = +2x + x = 3x and 4 - (-3) = 4 + 3 = 7.