(x^2-xy+5x-5y)/(x^2+5x), Can You Solve This?

Answer:
There doesn't appear to be anything to solve. However, the expression can be simplified somewhat.

First, look at the expression. The numerator has 3 terms containing x and 2 terms containing y. Both of the y expressions in the numerator have a negative sign. The denominator's vocabulary all contain x, so x can be factored out of the denominator to get denominator = x(x+5).

We can factor out -y from part of the numerator, and see what we enjoy left.
numerator = (x2-xy+5x-5y) = -y(x+5) + (x2+5x)

At this point, we recognize the (x+5) factor that was contained by the denominator, and we see that the remaining numerator terms can be factored along similar lines:
numerator = -y(x+5) + (x2+5x) = -y(x+5) + x(x+5) = (x-y)(x+5)

numerator/denominator = (x-y)(x+5)/(x(x+5)) = (x-y)/x    (after we divide out the x+5 factor from both numerator and denominator)

So, our simplified expression is
(x-y)/x  or  1-(y/x)    (the first is probably the preferred form; the second may be easier to calculate)


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