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factor 2x^2+7x-15 = (2x-3)(x-1)
factor x-5/2x^2-5x+3 = (2x-3)(x+5)
can you find the LCD now?
Seems more like a GCF than an LCD, doesn't it? Odd question...
so does this mean that the lcd is (2x-3)(x-1)(x+5)?
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I suppose so. If you had fractions where the first fraction had the first expression as a denominator and the 2nd fraction had the 2nd expression as its denominator, then the LCD would be the expression you just wrote...
The point, I guess, is that by factoring FIRST, you realize that (2x-3) is actually a common factor, and so you wouldn't multiply by that... if you just multiplied the original expressions together to try to get the LCD, it would be a common denominator, but it wouldn't be the LEAST one... it would be too big by an extra factor of (2x-3)