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[.5x^2-.6xy-.14x^2+.25y^2]/[1.2x+.7y-.6x-1.2y]

Take [.5x²-.6xy-.14x²+.25y²]/[1.2x+.7y-.6x-1.2y] and combine like terms.

There are two x² terms in the numerator (.5x² and -.14x²),

two x terms in the denominator (1.2x and -.6x),

and two y terms in the denominator (.7y and -1.2y).

Combining each pair of like terms gives [.36x² -.6xy + .25y²]/[0.6x-0.5y].

This is the same as (ax+by)² / (ax+by) where a=0.6 and b=-0.5.

An ax+by can be cancelled, leaving ax+by. That is, 0.6x - 0.5y.

If that is not recogninzed, multiply by 100/100 givig (36x² - 60xy + 25y²)/(60x-50y);

Doing long division, if we multiply 6x-5y by 6x, we get 36x² - 30xy.

Subtraction of this term from 36x² - 60xy + 25y² gives -30xy + 25y².

If we multiply 6x-5y by -5y, that is the answer.

That makes the fraction (6x-5y)(6x-5y)/[10(6x-5y)].

Cancelling the 6x-5y in the top and bottom leaves one in the top, so the (6x-5y)/10.

Dividing by 10 gives 0.6x - 0.5y, and that's the same as the previous result.

Algebra

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