SOLUTION: x to -2 power - y to -2 power divided by x to -1 power + y to -1 power (no parentheses in problem) answer is y - x divided by xy how do you get the answer

Question 558789: x to -2 power - y to -2 power divided by x to -1 power + y to -1 power
(no parentheses in problem)
answer is y - x divided by xy
how do you get the answer
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
As I understand your problem, you are to simplify the problem:
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Let's work on the numerator first by simplifying:
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From the rules of exponents, if you have a negative exponent you can convert that by dividing 1 by the same term with a positive exponent. Following that rule we can convert:
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to
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and similarly we can convert:
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to
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Substituting these into the expression you were given for the numerator converts the numerator to:
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The common denominator for this expression is . We can multiply the x-term by to change it to . Similarly we can multiply the y-term by to change it to .
Substituting these changed terms into the numerator makes it become:
.
and finally combining the two terms over the common denominator results in the numerator becoming:
.
<--- remember this numerator for later
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Now let's do a similar procedure for the denominator of the problem. We had a denominator of:
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We can convert these to positive exponential terms by placing the under 1 to get and the under 1 to get . This makes the denominator become:
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The common denominator for this is and when we place the two terms over this common denominator (by following the general process we used for the numerator) the result is:
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<--- this is now the denominator for the original problem
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We are now going to divide this denominator into the numerator that we remembered for later.
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The denominator is a fraction. Remember from long ago that you can divide by a fraction by inverting it and multiplying. So we can divide by inverting the denominator and multiplying it by the numerator we remembered. When we invert the denominator we get:
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Then multiplying this by the numerator the problem becomes:
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Notice that the numerator of the second term can be canceled with the denominator of the first term to just an in the denominator and make the expression become:
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Then notice that the is the difference of two squares. It can, therefore, be factored to to convert the expression to:
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Next notice and cross out the common factor in the numerator with a common factor in the denominator:
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and as a final step, when you multiply everything out you end up with:
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which is just as you said it should be.
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I hope that with a little careful tracking you can work your way through this and that it gives you some insight to the problem. Good luck ...
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