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

Answer
Take [.5x-.6xy-.14x+.25y]/[1.2x+.7y-.6x-1.2y] and combine like terms.
There are two x terms in the numerator (.5x and -.14x),
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 [.36x -.6xy + .25y]/[0.6x-0.5y].
This is the same as (ax+by) / (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 (36x - 60xy + 25y)/(60x-50y);
Doing long division, if we multiply 6x-5y by 6x, we get 36x - 30xy.
Subtraction of this term from 36x - 60xy + 25y gives -30xy + 25y.
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.

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Scott A Wilson

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Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.

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I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

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MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

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