Question

Can someone please help me to answer this math question? Please? I will fan and give a medal...
Please help me to simplify this Rational Expression -
8 3
------ - -----
x^2-4 x-2

Answer 1

hint: start by factoring x^2 - 4

Answer 2

it would be (2 + x)(-2 + x) right?

Answer 3

Yes. We would write that (x-2)(x+2)

Answer 4

To add or subtract fractions, the denominators have to be the same. So change the second fraction so that it has the same denominator.

Answer 5

good, then we convert both fractions to the same denominator

any ideas now?

Answer 6

So change
8 3
------ - -----
x^2-4 x-2
into
8 3
------ - -----
x-2 x-2

Answer 7

not quite, we can't do it like that

Answer 8

remember, in order to keep a fraction the same, we have to change the numerator and the denominator by the same operations

Answer 9

to go from

x - 2 to x^2 - 4, we have to multiply by (x+2)

Answer 10

\[\frac{8}{(x-2)(x+2)} - \frac{3}{x-2}\]
\[\frac{8}{(x-2)(x+2)}-\frac{3}{(x-2)}\times \frac{x+2}{x+2}\]

Answer 11

so...

3
---
x - 2

becomes

3(x-2)(x+2)
------
x^2 - 4

Answer 12

Can you take it from there?

Answer 13

what do I do after that? @Mertsj

Answer 14

Do you see that both denominators are now the same?

Answer 15

yes sir

Answer 16

So leave the denominators alone. Use the distributive property on the numerator of the second fraction.

Answer 17

What did you get?

Answer 18

3 x^2-6 x ? @Mertsj

Answer 19

3(x+2)= ?????