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$$\frac{3-{\sqrt 5}}{\sqrt 5 + 5}$$

This is probably ridiculously straightforward but I need to get to the answer $$ 1-\frac{2}{5}{\sqrt 5}$$

and can't figure out how to rationalise the denominator bc 5 - 5 = 0 and can't have that on the bottom of a fraction. pls help

Ma Ha
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  • $5-5=0$ is irrelevant. $\sqrt 5 - 5$ is not zero ... – Martin R Dec 18 '18 at 18:09
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    Multiplying by $5-\sqrt5$ the denominator becomes $5^2-5=20 \neq 0$. – Crostul Dec 18 '18 at 18:09
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    $$5^2-(\sqrt 5)^2 \neq 5-5$$ – KM101 Dec 18 '18 at 18:12
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    A general hint for future work: if you have two real numbers, neither of them is zero, and by multiplying them together you get zero, you made a mistake and should check your work. – David K Dec 18 '18 at 18:15
  • Wait ok maybe I didn't explain well- what I was trying to do was multiply the whole fraction by √5-5. (√5+5)(√5-5) on the bottom of the fraction would be zero because of the difference of squares – Ma Ha Dec 18 '18 at 23:38
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    OH hang on I get it, that was so dumb can't believe I didn't see that.. I'm starting maths from scratch and keep making silly mistakes haha. Thanks for your patience and answers! – Ma Ha Dec 18 '18 at 23:47

1 Answers1

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Write $$\frac{(3-\sqrt{5})(5-\sqrt{5})}{(5+\sqrt{5})(5-\sqrt{5})}=...$$

Dr. Sonnhard Graubner
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