Question 23358: Hi, can you help me solve
3x-2 2
————— - —————
x+2 x-2
Found 2 solutions by rapaljer, AnlytcPhil: Answer by rapaljer(4671) (Show Source): Answer by AnlytcPhil(1806) (Show Source):
You can put this solution on YOUR website! Hi, can you help me solve
3x-2 2
————— - —————
x+2 x-2
We want to cause both those denominators to become the LCD, which is
(x+2)(x-2). We use the principle:
If you multiply the numerator and denominator of a fraction by the
same thing you don't change the value of the fraction. You only change
its looks.
The first fraction has denominator x+2. It needs to become the LCD,
which is (x+2)(x-2), so it needs to be multiplied by (x-2).
I can do this without changing the fraction's value if I'll also
multiply the numerator by (x-2).
So the first fraction:
3x-2
—————
x+2
becomes
(3x-2)(x-2)
———————————
(x+2)(x-2)
FOIL the top out but DON'T FOIL the bottom!
3x²-8x+4
——————————
(x+2)(x-2)
Now the second fraction has denominator x-2. It needs to become
the LCD, which is (x+2)(x-2), so it needs to be multiplied by (x+2).
I can do this without changing the fraction's value if I'll also
multiply the numerator by (x+2) also.
Now the second fraction:
2
—————
x-2
becomes
2(x+2)
———————————
(x-2)(x+2)
Multiply the top out but not the bottom!
2x+4
——————————
(x-2)(x+2)
Now back to the original problem:
3x-2 2
————— - —————
x+2 x-2
becomes
3x²-8x+4 2x+4
—————————— - ——————————
(x+2)(x-2) (x-2)(x+2)
Now the denominators are equal.
So we subtract the numerators, placed first in parentheses,
then write that over the common denominator.
(3x²-8x+4) - (2x+4)
———————————————————
(x+2)(x-2)
Now remove the parentheses on top and collect terms. Leave
the bottom as it is:
3x²-8x+4-2x-4
———————————————————
(x+2)(x-2)
3x²-10x
———————————————————
(x+2)(x-2)
That's good enough. You can leave it like that. But if you
like you can factor out x on the top.
x(3x-10)
—————————————————
(x+2)(x-2)
In some problems, doing that produces something that will cancel,
but that didn't happen this time. For instance, if that (3x-10)
had been (x+2) or (x-2) instead it would have canceled. But it
wasn't so it didn't.
Edwin
AnlytcPhil@aol.com
|
|
|