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    Rationalise the denominator

    (√(a+1)-√a)
    (√(a+1)+√a)

    Please help
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    (Original post by Nasir.)
    Rationalise the denominator

    (√(a+1)-√a)
    (√(a+1)+√a)

    Please help
    you need to multiply the fraction by

    (√(a+1)-√a)
    (√(a+1)-√a)

    then simplify
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    Use (x + y)(x - y)=x^2 - y^2

    What could you multiply by that would remove surds from the denominator?
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    (Original post by Tbarker1)
    you need to multiply the fraction by

    (√(a+1)-√a)
    (√(a+1)-√a)

    then simplify
    I did. Its all gone messy.
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    (Original post by RogerOxon)
    Use (x y)(x-y)=x^2 y^2

    What could you multiply by that would remove surds from the denominator?
    By the surds themselves?
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    I have tried several times, I don't know where I am going wrong how do you multiply three terms with another three terms.
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    (Original post by Nasir.)
    By the surds themselves?
    I've corrected the TeX in my post now - the Android app is really nasty.

    You've been given the next step by Tbarker1. Note that (\sqrt{a+1} + \sqrt{a})(\sqrt{a+1} - \sqrt{a}) = a+1 - a = 1

    The denominator is of the form a+b, so if you multiply by \frac{a-b}{a-b} (which is 1, when a and b aren't equal), it'll reduce the denominator to a^2-b^2, removing the surds.
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    (Original post by RogerOxon)
    I've corrected the TeX in my post now - the Android app is really nasty.

    You've been given the next step by Tbarker1. Note that (\sqrt{a+1} + \sqrt{a})(\sqrt{a+1} - \sqrt{a}) = a+1 - a = 1
    You might initially find it simpler to rewrite the equation using x=\sqrt{a+1} and y=\sqrt{a} - it'd save writing square roots all over the place, until you get to the stage where you can simplify further. Otherwise, I prefer using a half power rather than a square root sign - IMO, it's less messy.
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    in general usually, the goal is to try to make a difference of two squares on the denominator. to cancel out the surds
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    (Original post by Nasir.)
    I did. Its all gone messy.
    Try entering the equation into symbolab (a website). It'll give you all the steps and the solution.
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    Its still gone messy. It's fine, I am going to take a rest and do the question tomorrow, maybe convert the roots into indices instead and have a go.
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    Not getting it. Sorry.
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    what don't you get?
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    (Original post by Nasir.)
    I have tried several times, I don't know where I am going wrong how do you multiply three terms with another three terms.
    What are the three terms? Tbarker1 has posted a correct solution, although I wouldn't have written it slightly differently, as 2a+1 + \sqrt{a(a+1)}
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    (Original post by Tbarker1)
    ......
    Please edit your post - it is against the rules to post a solution
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    (Original post by RogerOxon)
    Does this help? ...

    Please read the rules
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    (Original post by Muttley79)
    Please read the rules
    Rules are for the obeyance of fools and ..

    To be fair, a complete solution had already been posted and, after lots of hints / direction, the OP was still not getting anywhere.
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    IMO this thread would have gone a lot better if someone asked the OP to post their working.
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    (Original post by Notnek)
    IMO this thread would have gone a lot better if someone asked the OP to post their working.
    Exactly!
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    (Original post by RogerOxon)
    Does this help?

    Let:

    x=\sqrt{a+1}

    y=\sqrt{a}

    So,

    \frac{x-y}{x+y}=\frac{x-y}{x+y} \frac{x-y}{x-y}=\frac{(x-y)^2}{x^2-y^2}=\frac{x^2-2xy+y^2}{x^2-y^2}

    =\frac{a+1 - 2\sqrt{a} \sqrt{a+1} + a}{a+1 - a}=2a+1 - 2\sqrt{a(a+1)}
    Name:  WIN_20181017_21_21_19_Pro.jpg
Views: 10
Size:  97.3 KB

    I understand the xy format but I don't understand how it came to this way. See my working please and let me know where I am going. Many thanks
 
 
 

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