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Topic: Please help me simplify this expression.
Replies: 5   Last Post: Jan 24, 2005 2:20 AM

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ticbol

Posts: 116
Registered: 1/25/05
Re: Please help me simplify this expression.
Posted: Jan 24, 2005 2:18 AM
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Look at this:

[x(x+2)^-(1/2) + (x+2)^(1/2) ] / (x+2)^(3/2)

We clear the negative exponent,
= [x/(x+2)^(1/2) + (x+2)^(1/2) ] / (x+2)^(3/2)

We simplify those inside the bracket,
= [{x +(x+2)^(1/2)* (x+2)^(1/2)} / {(x+2)^(1/2)} ] / (x+2)^(3/2)
= [{x +(x+2)^1} / {(x+2)^(1/2)} ] / (x+2)^(3/2)
= [{x +x+2} / {(x+2)^(1/2)} ] / (x+2)^(3/2)
= [{2x +2} / {(x+2)^(1/2)} ] / (x+2)^(3/2)
= [{2(x+1)} / {(x+2)^(1/2)} ] / (x+2)^(3/2)

We carry on,
= [{2(x+1)} / {(x+2)^(1/2)} ] * [1/ (x+2)^(3/2)]
= [2(x+1)] / [{(x+2)^(1/2)} * {(x+2)^(3/2)}]
= [2(x+1)] / [(x+2)^(4/2)]
= 2(x+1) / (x+2)^2 -----answer.


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