I need to learn how to find the least common denominator with 3 different fractions that have variables included.
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3/x + 2/(x+1) + 5/(x+2)
The least common denominator is the product of the 3 denominators:
LDC = x(x+1)(x+2)
Now we have to multiply each fraction by the missing part of the LCD:
(3/x)(x+1)(x+2)/(x+1)(x+2) + (2/(x+1))(x(x+2)/x(x+2) + (5/(x+2)(x/(x+1)/x(x+2))
= [3(x+1)(x+2) + 2x(x+2) + 5x(x+1)] / x(x+1)(x+2)
= [3x^2+9x+6+2x^2+2x+5x^2+5] / x(x+1)(x+2)
= 10x^2+11x+11 / x(x+1)(x+2)
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