Question

quick question... \[\frac{x^2}{x^2 - 4}- \frac{x+1}{x+2}\] LCD is \(x^2 - 4\) or \(x+2\)??

Answer 1

thanks :D

Answer 2

the LCD is x^2 - 4 because x+2 and x^2 - 4 divide it cleanly.

Answer 3

im confused o.O how do you know the LCD?

Answer 4

the LCD is what we learned when we were taught how to add/subtract fractions with different denominators.

Answer 5

x^2 - 4 --> isnt it the LCM ?

Answer 6

in this case, the LCM and the LCD are the same

Answer 7

uhmm but how do you find the LCD of rational expressions?

Answer 8

\(\Large \color{purple}{\rightarrow {a \over b} \pm {c \over d} = {ad \pm cb \over bd} }\)

Answer 9

we must have the same denominator if we want to add/subtract numerators, so multiply the fraction on the right by (x-2)/(x-2) to get the LCD

Answer 10

so shouldnt it be (x^2-4)(x+2)??

Answer 11

@ParthKohli

Answer 12

no, because x^2 - 4 is a difference of squares, = (x-2)(x+2)

Answer 13

why x-2?

Answer 14

i mean when you multiply the right by x-2/x-2

Answer 15

we're essentially multiplying the fraction on the right by 1 to get the same denominator as the fraction on the left

Answer 16

but why x-2?

Answer 17

because (x+2)(x-2) = the denominator of the fraction on the left

Answer 18

ohhh we multiply something to make it look like that so x-2

Answer 19

ok thanks ^_^

Answer 20

\(\Large \color{purple}{\rightarrow x^2 - 4 = x^2 - 2^2 = (x + 2)(x - 2) }\)