Add or subtract, as indicated. (x + y)/(2x - y) - 2x/(y - 2x)

Question

Accepted Answer

Hey everyone here we are asked to subtract the following and simplify the answer of H plus three K. All divided by h minus nine k minus seven H. Divided by nine k minus H. So now taking a look at our given expression, we see that in order to subtract these two fractions from each other we need to have a common denominator so we can take a closer look at our second denominator here where we have nine k minus H. Well if we factor out a negative one from this denominator we can rewrite this expression as negative one times the quantity of h minus nine K. So now we want to substitute in this new expression for our second denominator. And so doing this our expression becomes H plus three K. All divided by h minus nine k minus seven H. Divided by negative one times the quantity of h minus nine K. And now looking at our second fraction here we we see that we have this negative one. This negative term in the denominator and we also have a negative seven H. In the numerator. So with these negative terms in the numerator and the denominator our entire second fraction becomes positive. So rewriting our expression, we have H plus three K. All divided by H minus nine K. Plus seven H. Divided by h minus nine K. And now taking a look at both fractions, we see that we have common denominators so we can go ahead and perform the operation between the numerator. So doing this we have H plus three K from our first numerator plus our second numerator which is seven H. And this is all divided by the common denominator of H minus nine K. And so now we just need to simplify by combining like terms and we see that in the numerator we get three K plus eight H. All divided by h minus nine K. And with this we have fully simplified our answer. There aren't any other simplifications that we can make. So this is our final answer here which is answer choice C. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Add or subtract, as indicated. (x + y)/(2x - y) - 2x/(y - 2x)

Key Concepts

Rational Expressions

Common Denominator

Simplifying Expressions

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