Fun with Algebra...

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birdpoop: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sun Oct 05, 2008 5:50 pm

by birdpoop » Mon Oct 06, 2008 4:44 pm

Please, break down the algebra for me:

(1)

If x NOT EQUAL to 2, then (3x^2(x-2) - x + 2) / x - 2 = ??????

(2)

Solve for y: x+y / xy = 1

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Source: Beat The GMAT — Problem Solving | Mon Oct 06, 2008 4:44 pm

PussInBoots: Master | Next Rank: 500 Posts; Posts: 157; Joined: Tue Oct 07, 2008 5:47 am; Thanked: 3 times

by PussInBoots » Tue Oct 07, 2008 5:59 am

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

Remember that -a + b = - (a - b)
(2): (x + y) / (xy) = 1
[(x+y) * (1/y)] / [(xy) * (1/y)] = 1
(x/y + 1) / x = 1
x/y + 1 = x
x/y = x-1
y/x = 1/(x-1)
y = x/(x-1)

P.S.: simple use of rule a / b = (a * c) / (b * c), c !=0

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