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Anna71 [15]
2 years ago
5

Simplify 4/(√5+ √2) - 3/(√5- √2)​

Mathematics
1 answer:
MakcuM [25]2 years ago
8 0

Step-by-step explanation:

\frac{4}{ \sqrt{5} +   \sqrt{2}}  -  \frac{3}{ \sqrt{5} -  \sqrt{2}  }  =  \\  =  \frac{4( \sqrt{5}  -  \sqrt{2} ) - 3( \sqrt{5} +  \sqrt{2} ) }{( \sqrt{5}  +  \sqrt{2}  )\times ( \sqrt{5}  -  \sqrt{2} )}  =  \\  =  \frac{4 \sqrt{5} - 4 \sqrt{2}  - 3 \sqrt{5} - 3 \sqrt{2}   }{5 -  \sqrt{10}  +  \sqrt{10} - 2 }  =  \\  =  \frac{ \sqrt{5}  - 7 \sqrt{2} }{3}

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