Question 5262
<font face = "courier new" size = 3>I could not find any lessons for my brother on
Adding and Subtracting algebraic fractions. Could
you please help me. Could you also show me how to 
type in fractions. In this problem x is under x+2 
then you add with x+1 under x. Thank you
`<b>
x+2` ` x
--- + ---
`x ` `x+1
`
Put parentheses around the first numerator and the 
second denominator because they contain 2 terms
`
(x+2)` ` `x
----- + -----
` x` ` `(x+1)
`
The LCD is x(x+1)
The first denominator is x.  Thus to become equal to 
the LCD it needs to be multiplied by (x+1). But we 
must multiply both the numerator and the denominator 
by (x+1), so that it will amount to multiplying by 1.
`
(x+2)`(x+1)` ` `x
-----·----- + -----
` x` `(x+1)` `(x+1)
`
Multiply out the (x+2)(x+1) using the FOIL method,
(x+2)(x+1) = x²+1x+2x+2 = (x²+3x+2).  Do not multiply
out the denominator x(x+1), but just leave it as it is
`
(x²+3x+2) ` ` x
--------- + -----
` x(x+1)` ` (x+1)
`
The second denominator is x.  Thus to become equal to
the LCD it needs to be multiplied by x. But we must 
multiply both the numerator and the denominator by x, 
so that it will amount to multiplying by 1.
`
(x²+3x+2)` ` `x ` `x
--------- + -----·---
` x(x+1)` ``(x+1)` x
`
Multiply the x by the x, getting x².  Do not multiply
out the denominator (x+1)x, but write it as x(x+1)
`
(x²+3x+2)` ` `x²    
--------- + ------
` x(x+1)` ` x(x+1)
`
Now both fractions have the same LCD, so we
combine the numerators and place it over the LCD
`
(x²+3x+2)+x²    
------------
` x(x+1) 
`
Remove the parentheses
`
x²+3x+2+x²
----------
` x(x+1)

Combine the x² and the x², getting 2x²
`
2x²+3x+2
--------
`x(x+1)
`
The numerator does not factor, so we are done.
`
Edwin