SOLUTION: The area of the rectangle is 2(3x-2)/x-1 Find the width.

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Question 107624: The area of the rectangle is 2(3x-2)/x-1 Find the width.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The area (A) of the rectangle is 2%283x-2%29%2F%28x-1%29
Find the width
length%2Awidth+=+2%283x-2%29%2F%28x-1%29 =>

Let length be 2%283x-2%29%2F%282x-2%29

Since length++%2Awidth+=+areathen we have:

%282%283x-2%29%2F%282x-2%29%29+%2A+width+=+2%283x-2%29%2F%28x-1%29

width+=+%282%283x-2%29%2F%28x-1%29%29%2F%282%283x-2%29%2F%282x-2%29%29....the %283x+-+2%29 factors cancel out

width+=+%282%2F%28x-1%29%29%2F%282%2F%282x-2%29%29....the 2facors cancel out

width+=+%282x-2%29%2F%28x-1%29..........


or this way:
if length%2Awidth+=+2%283x-2%29%2F%28x-1%29 => ...we have a rational expression on right side
.... we know that a product of two numbers (or expressions) is rational number (expression)in case when both numbers (expressions) are rational, or when one number (expression) is whole number and other one is rational.
so, if we say that length+=+2%283x+-2%29,

then with must be 1%2F%28x-1%29
because only %282%283x-2%29%29%2A%281%2F%28x-1%29%29 will give us 2%283x-2%29%2F%28x-1%29