What is the LCD of x and x+h?

ClassyCorgi

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Two fractions have the denominators x, and x+h. I need to find the Least Common Denominator of the two in order to subtract rational expressions. How do I find the LCD of two expressions that only have variables, not numbers?
 
Two fractions have the denominators x, and x+h. I need to find the Least Common Denominator of the two in order to subtract rational expressions. How do I find the LCD of two expressions that only have variables, not numbers?
To learn how to find LCMs (and GCFs) in general, try here. ;)
 
Two fractions have the denominators x, and x+h. I need to find the Least Common Denominator of the two in order to subtract rational expressions. How do I find the LCD of two expressions that only have variables, not numbers?

To add/subtract fractions you need to get a common denominator. (It doesn't have to be the least common denominator.)
So your common denominator would be x(x+h) ie simply multiply them together.
 
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But why is this the common denominator? How does the student find this on his/her own? ;)

I'm not sure how to answer your first question without going right back to the basics of fractions. I have assumed that the student can add numerical fractions but is having difficulty with algebraic ones.
 
perhaps this will help

Two fractions have the denominators x, and x+h. I need to find the Least Common Denominator of the two in order to subtract rational expressions. How do I find the LCD of two expressions that only have variables, not numbers?

y = a/x + b/(x+h)

multiply both sides by the "Common Denominator" = x(x+h)

y x (x+h) = a(x+h) + bx

multiply both sides by the Common Denominator's multiplicative inverse = 1/(x(x+h))

y = (a(x+h) + bx) / (x(x+h))
 
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