Question

Find the following difference:

Answer 1

question....?

Answer 2

\[\frac{ 6 }{ x+8 }-\frac{ 48 }{ x^2-64 }\]

Answer 3

Sorry, thought I posted it.

Answer 4

a/d-b/c = (ad-bc)/bd

Answer 5

\[\frac{ 6(x+8)-48(x^2-64) }{ 48(x+8) }\]

Answer 6

To add or subtract fractions, you need a common denominator.
Can you factor the right denominator?

Answer 7

like this, @iambatman ?

Answer 8

No.
Instead of following a complicated formula you will most likely forget, follow my steps and we'll work it out together.

Answer 9

ok, let's do this...
(x+6)(x-6)

Answer 10

6? I think you mean 8.
(x + 8)(x - 8) right?

Answer 11

lol, yes, i meant 8, sorry...family guy is on lol

Answer 12

Ok, we can write one step where the right denominator is factored.

\(\dfrac{ 6 }{ x+8 }-\dfrac{ 48 }{ x^2-64 }\)

\(=\dfrac{ 6 }{ x+8 }-\dfrac{ 48 }{ (x + 8)(x - 8) }\)

Answer 13

Now we need a common denominator.
What is the LCD of x + 8 and (x + 8)(x - 8) ?

Answer 14

x+8?

Answer 15

x + 8 is what the two denominators have in common.
We need the least common denominator.
You need one factor of each.
The LCD is (x + 8)(x - 8)

Answer 16

oh ok

Answer 17

Notice, the right fraction already has the LCD as its denominator.
The left denominator is only x + 8, so we multiply the left fraction by \(\dfrac{x - 8}{x - 8} \)

Answer 18

\(= \dfrac{ 6 }{ x+8 } \cdot \dfrac{ x - 8 }{ x-8 }-\dfrac{ 48 }{ (x + 8)(x - 8) }\)

Answer 19

\[\frac{ 6x-48 }{ (x+8)(x-8) }-\frac{ 48 }{ (x+8)(x-8) }\]
Right?

Answer 20

\(= \dfrac{ 6 (x - 8)}{( x+8)(x-8) } -\dfrac{ 48 }{ (x + 8)(x - 8) }\)

\(= \dfrac{ 6 x - 48 }{( x+8)(x-8) } -\dfrac{ 48 }{ (x + 8)(x - 8) }\)

Answer 21

You're ahead of me. You catch on fast!

Answer 22

Now we actually do the subtraction. We subtract the numerators, and set is all over the common denominator.

Answer 23

So, -48-48?

Answer 24

It's not a complicated formula, it's just how fractions are done lol.

Answer 25

What happened to the 6x?

Answer 26

\(= \dfrac{ 6 x - 48 - 48}{( x+8)(x-8) } \)

Answer 27

I have no idea what happened to the 6x, but ok, so 6x-48-48? I'm lost again

Answer 28

That's good.
Now combine the -48 and -48 since they are like terms.

Answer 29

\(= \dfrac{ 6 x - 96}{( x+8)(x-8) } \)

Answer 30

now, I factor the top?

Answer 31

The last line above is already a correct answer.
If you want to, you may factor the numerator.
You can also multiply out the denominator.

Answer 32

\(= \dfrac{ 6 x - 96}{ x^2 - 64 } \)

Personally, i like it like this.

Answer 33

It involves the least amount of writing.

Answer 34

lol I already typed in the first answer lol thanks!

Answer 35

Like I said, any form is correct.
You're welcome.

Answer 36

@iambatman

You claim this is how fractions are done:
\(\dfrac{a}{ d} - \dfrac{b}{ c} = \dfrac{ ad-bc }{ bd} \)

Let's see if it works.

\(\dfrac{a}{ d} - \dfrac{b}{ c} \)

\(=\dfrac{a}{ d} \cdot \dfrac{c}{c} - \dfrac{b}{ c} \cdot \dfrac{d}{d} \)

\(=\dfrac{ac}{ dc} - \dfrac{bd}{ cd} \)

\(=\dfrac{ac - bd}{ dc} \ne \dfrac{ ad-bc }{ bd}\)

As you can see, your formula is not correct.

You got the formula wrong because you wrote the two fractions to be subtracted incorrectly. This is what you meant to write.

\(\dfrac{a}{ b} - \dfrac{c}{ d} = \dfrac{ ad-bc }{ bd}\)

Instead of memorizing a formula to do a simple thing, I'd rather just do it. You just proved my point. By writing the formula incorrectly, you'd subtract the fractions incorrectly.

Answer 37

Relax I wrote it wrong by accident, I was in a rush.

\[\frac{ a }{ b }-\frac{ c }{ d } => \frac{ ad-bc }{ bd }\]

This is what I meant.