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# Simplify

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Simplify. Is this correct?

My answer = c^2 + d^2

Guest Mar 10, 2015

#3
+20009
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$$\small{\text{  \dfrac{ \dfrac{c}{d}-\dfrac{d}{c} } { \dfrac{1}{c}-\dfrac{1}{d} } = \dfrac{ \dfrac{c^2-d^2}{dc} } { \dfrac{d-c}{dc} } = \left( \dfrac{c^2-d^2}{dc} \right) \cdot \left( \dfrac{dc}{d-c} \right) = \dfrac{c^2-d^2}{d-c} = -\dfrac{c^2-d^2}{c-d} = -\dfrac{(c-d)\cdot (c+d) }{c-d} = - (c+d) }}\\\\$$

heureka  Mar 11, 2015
#3
+20009
+10

$$\small{\text{  \dfrac{ \dfrac{c}{d}-\dfrac{d}{c} } { \dfrac{1}{c}-\dfrac{1}{d} } = \dfrac{ \dfrac{c^2-d^2}{dc} } { \dfrac{d-c}{dc} } = \left( \dfrac{c^2-d^2}{dc} \right) \cdot \left( \dfrac{dc}{d-c} \right) = \dfrac{c^2-d^2}{d-c} = -\dfrac{c^2-d^2}{c-d} = -\dfrac{(c-d)\cdot (c+d) }{c-d} = - (c+d) }}\\\\$$

heureka  Mar 11, 2015
#4
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Thanks. That's the answer I also got, when I tried it the second time. :)

Guest Mar 11, 2015