algebra
posted by sid .
when adding or subtracting rational exprssions, why do you need an LCD

The rules for numerators and denominators are different. When adding or subtracting fractions, or fractional algebraic terms, the denominators must be the same. Then, you can add or subtract the numerators while keeping the common denominator.
The reason should be obvious when you think about it. When you have a series of numbers with the same denominator x, the ratio of their sizes is the ratio of the numerators.
Thus a/x + b/x = (a+b)*(1/x) = (a+b)/x
You cannot write an analogous valid expression to justify adding denominators with a common numerator. instead, you have
x/a + x/b = x(1/a + 1/b), = x(b+a)/ab 
3 4/9 x 1 4/5 show work please
Respond to this Question
Similar Questions

Algebra
Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator. 3 5 ,  84a 63b 4b 6 ,  75a 105ab Can someone here help me … 
Help1
WHY rational expressions that are being added must have an LCD, but rational expressions that are being multiplied do not need to have an LCD. The short answer is that addition and multiplication are different operations with different … 
algebra
Reduce to lowest terms 3x6/x^24x+4 perform operation w^21/(w1)2 times w1/w^2+2w+1 Find LCD and convert rational express. to equivalent rat. exp. with LCD as the denominator: 4/a6 , 5/6a 
algebra
Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator. 4/xy , 5/2y2x 
Math
When adding and subtracting rational expressions, why do you need a LCD? 
adding and subtracting rational
5/6+4/9= 
adding and subtracting rational
10 11/127 1/4= 
adding and subtracting rational
11/15+1/8= 
adding and subtracting rational
15/163/4= 
precalculus 11
x/(x3) + 2x/(x+2) (x1) x (x2) (x+2)/(x3)(x3) my question is should i multiply first and then do the adding or subtracting through a LCD or should i do the adding first?