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Old 08-05-2007   #1
Heller
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Default Please help with this math question and show all the work:

-5/2x(x+3)^(-3/2)+5(x+3)^(-1/2)? -5/2x(x+3)^(-3/2)+5(x+3)^(-1/2)-5/2x(x+3)^(-3/2)+5(x+3)^(-1/2) The question says to simplify-5/2x(x+3)^(-1.5)+5(x+3)^(-.5) The question says to simplify
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Old 08-05-2007   #2
Oyvind J
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First observe that the second addend (5(x+3)^(-1/2) = 5 / sqrt(x+3)) is a common factor in the two addends.Rewrite the statement:[5 / sqrt(x+3) ] * [1 / (2x + (x+3)^2) +1]Explode the squared parenthesis (x+3)^2:[5 / sqrt(x+3) ] * [1 / (2x + x^2+6x +9) +1]contract the 6x-statement from the explosion with the 2x:[5 / sqrt(x+3) ] * [1 / (x^2+8x +9) +1]Now replace the "+1" with "+ (x^2 + 8x +9) / (x^2 + 8x +9)"and rewrite:[5 / sqrt(x+3) ] * [1 / (x^2+8x +9) + (x^2 + 8x +9) / (x^2 + 8x +9)]The second factor now has a common denominator.Contract the second factor:[5 / sqrt(x+3) ] * [(1+ x^2 + 8x +9) / (x^2 + 8x +9)][5 / sqrt(x+3) ] * [(x^2 + 8x +10) / (x^2 + 8x +9)]and multiply the two factors into a simplified statement:[5 / sqrt(x+3) ] * [(x^2 + 8x +10) / (x^2 + 8x +9)]5 * (x^2 + 8x +10)------------------------------------sqrt(x+3) * (x^2 + 8x +9)](5x^2 + 40x +50) --------------------------------- (x^2 + 8x +9) * sqrt (x+3)Now, use x = [-b +- sqrt(b^2-4ac)] / 2a to factorize the second order statements in the numerator and denominator. I leave that up to you.Good luck.
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