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It is similar on dividing whole numbers.

let y = x² + 4x - 12 / x - 2

Step 1:
Divide the first term of the dividend to that of the first term of the divisor.
x² / x = x
The quotient will be the first term of your answer. 

Step 2:
Multiply first the quotient by the terms of the divisor.
x(x) = x² 
x(-2) = -2x 
And then put it below the terms of the dividend.

Step 3:
Subtract the terms of the divisor by the product. 
x² - x² = 0
4x - (-2x) = 6x

Step 4:
Bring down one term left next to the difference.
6x - 12

Step 5:
Then go, repeat to step 1.

y =  x + 6
Now, can you get it? :)
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