Need help with this compound fraction

Kalebb

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I need some help with solving this compound fraction. I know I need to multiply all the fractions in the numerator and denominator by the LCD, which I believe is y^2 (right?) This gives me x^2-y^2 as the num and y^2 as the denom on the top. Then on the bottom I think I need to multiply the x/y by y (to get the same denominator y^2 as the top, right?) Which gives me xy+y^2 as the num and y^2 as the denom. Then I invert the second fraction to multiply instead of divide it. After canceling out the common factors I get x-y/y^2, but my book says the answer is x-y/y!? Does anyone know where I'm messing up in this? Compound fractions were the hardest thing to do in this chapter but they had only one example for me to look at and work through. Any help would be greatly appreciated.

Sincerely, a dumb college student who put off algebra until his last semester.

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I need some help with solving this compound fraction. I know I need to multiply all the fractions in the numerator and denominator by the LCD, which I believe is y^2 (right?) This gives me x^2-y^2 as the num and y^2 as the denom on the top. Then on the bottom I think I need to multiply the x/y by y (to get the same denominator y^2 as the top, right?) Which gives me xy+y^2 as the num and y^2 as the denom. Then I invert the second fraction to multiply instead of divide it. After canceling out the common factors I get x-y/y^2, but my book says the answer is x-y/y!? Does anyone know where I'm messing up in this? Compound fractions were the hardest thing to do in this chapter but they had only one example for me to look at and work through. Any help would be greatly appreciated.

Sincerely, a dumb college student who put off algebra until his last semester.

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Can you solve the following arithmetic problem:

\(\displaystyle \displaystyle{\dfrac{\frac{9}{4}-1}{\frac{3}{2} + 1}}\) = ?

Follow the same process. If you are still stuck, write back (including your work).
 
I need some help with solving this compound fraction. I know I need to multiply all the fractions in the numerator and denominator by the LCD, which I believe is y^2 (right?) This gives me x^2-y^2 as the num and y^2 as the denom on the top. Then on the bottom I think I need to multiply the x/y by y (to get the same denominator y^2 as the top, right?) Which gives me xy+y^2 as the num and y^2 as the denom. Then I invert the second fraction to multiply instead of divide it. After canceling out the common factors I get x-y/y^2, but my book says the answer is x-y/y!? Does anyone know where I'm messing up in this? Compound fractions were the hardest thing to do in this chapter but they had only one example for me to look at and work through. Any help would be greatly appreciated.

Sincerely, a dumb college student who put off algebra until his last semester.

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Lets do another example:
\(\displaystyle \dfrac{\dfrac{x}{y}\, -\, \dfrac{y}{x}}{1\, +\, \dfrac{y}{x}}\)
Now the LCD for the numerator is x y so lets start with that and only work on the numerator at first
numerator = \(\displaystyle \left [\frac{x}{y}\, -\, \frac{y}{x}\right ]\, x\, y\, =\, x^2\, -\, y^2\)
Now the denominator (multiplying through by the same LCD as the numerator)
denominator = \(\displaystyle \left [1\, +\, \frac{y}{x}\right ]\, x\, y\, =\, [x\, +\, y]\, y\)
since we only need the x to clear the fraction in the denominator, we have the y left outside the brackets.

So now we have
\(\displaystyle \dfrac{numerator}{denominator}\, =\, \dfrac{x^2\, -\, y^2}{[x\, +\, y]\, y}\)

Now, quoting Denis. "You do know that a^2 - b^2 = (a+b)(a-b), right?"
 
I need some help with solving this compound fraction. I know I need to multiply all the fractions in the numerator and denominator by the LCD, which I believe is y^2 (right?) This gives me x^2-y^2 as the num and y^2 as the denom on the top. Then on the bottom I think I need to multiply the x/y by y (to get the same denominator y^2 as the top, right?) Which gives me xy+y^2 as the num and y^2 as the denom. So far so good.

Then I invert the second fraction to multiply instead of divide it. At this stage you should have x^2-y^2 on the top and xy+y^2 on the bottom.

After canceling out the common factors I get x-y/y^2 Nope! After factorising you should have (x+y)(x-y) on the top and y(x+y) on the bottom

but my book says the answer is x-y/y!? Cancelling the common factor (x+y) will leave you with \(\displaystyle \frac{x-y}{y}\) or (x-y)/y

Does anyone know where I'm messing up in this? Compound fractions were the hardest thing to do in this chapter but they had only one example for me to look at and work through. Any help would be greatly appreciated.

Sincerely, a dumb college student who put off algebra until his last semester.

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