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# expanding this rational expression?

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Here's the expression: $$({2x -5 \over 5 -x })({5-x \over 5 -x })$$

Did I solve this right? Here's what I did:

$${ 10x - 2x^2 - 25 + 5x \over 25 - 5x -5x + x^2}$$

$${-2x^2 + 15x -25\over x^2 -10x +25}$$ (this is my answer)

Mar 31, 2018

#1
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You're right that   $$(\frac{2x-5}{5-x})(\frac{5-x}{5-x})$$  is equivalent to  $$\frac{-2x^2+15x-25}{x^2-10x+25}$$

....What do the full directions say?

Mar 31, 2018
#3
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"Create three sample expressions written in the form $${ax^2 + bx + c \over dx^2 + ex + f}$$ where the numerators and denominators factor and the expressions can be simplified." That was just one of them, and I wanted to make sure if my answer was right :)

Guest Apr 1, 2018
#4
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Ah thank you for the response! I didn't know whether it wanted the expression in simplest form.....but since it doesn't, your answer is correct!

hectictar  Apr 1, 2018
#2
+101032
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$$({2x -5 \over 5 -x })({5-x \over 5 -x })={2x -5 \over 5 -x }$$

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Mar 31, 2018