confusing geometry problem. someone help me with the steps

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dzelkas: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Jun 05, 2007 1:29 pm

by dzelkas » Fri Sep 21, 2007 1:50 pm

Can someone help me figure this out? I got confused on couple of steps..

x=(yz)/x+1/y
we are asked to find Z

here is the solution where i got confused

x-1/y=yz/x

x^2-x/y^2=z ( i got lost here. it looks like we multiplied by x to get rid of denominator but where did we get y^2 from?

x^2 y/y^2 - x/y^2=z ( again i got lost here)

z= x(xy-1)/y^2

can someone help me understand this little bit better. I would really appreciate it

thanks

danny

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Source: Beat The GMAT — Problem Solving | Fri Sep 21, 2007 1:50 pm

kajcha: Master | Next Rank: 500 Posts; Posts: 321; Joined: Tue Aug 28, 2007 5:42 am; Thanked: 1 times

by kajcha » Fri Sep 21, 2007 2:43 pm

x-1/y=yz/x

=> (x^2-x)/y = yz

=> z = (x^2-x)/(y^2)

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vsravan.2000: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Mon Dec 31, 2007 7:48 am

Re: confusing geometry problem. someone help me with the ste

by vsravan.2000 » Mon Dec 31, 2007 2:45 pm

dzelkas wrote:Can someone help me figure this out? I got confused on couple of steps..

x=(yz)/x+1/y
we are asked to find Z

here is the solution where i got confused

x-1/y=yz/x

x^2-x/y^2=z ( i got lost here. it looks like we multiplied by x to get rid of denominator but where did we get y^2 from?

x^2 y/y^2 - x/y^2=z ( again i got lost here)

z= x(xy-1)/y^2

can someone help me understand this little bit better. I would really appreciate it

thanks

danny

Hi

x-1/y = yz/x...(1)

Multiply with x on both sides with x=> x(x-1/y) = (yz/x)*x
= x^2 - x/y = yz.

Now devide with y on both sides with y to get rid of y on the right hand side of (1)
(x^2-x/y) /y = yz/y.
(x^2/y - x/y*1/y) =z
x^2/y - x/(y^2) = z . this is the answer

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preciousrain7: Senior | Next Rank: 100 Posts; Posts: 78; Joined: Thu Dec 06, 2007 4:16 pm; Location: NYC, NY; Thanked: 2 times

Re: confusing geometry problem. someone help me with the ste

by preciousrain7 » Tue Jan 08, 2008 5:30 pm

vsravan.2000 wrote:
Hi

x-1/y = yz/x...(1)

Multiply with x on both sides with x=> x(x-1/y) = (yz/x)*x
= x^2 - x/y = yz.

Now devide with y on both sides with y to get rid of y on the right hand side of (1)
(x^2-x/y) /y = yz/y.
(x^2/y - x/y*1/y) =z
x^2/y - x/(y^2) = z . this is the answer

How do you guys get x-1/y = yz/x ? How can you turn x+1 into x-1?

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