Question

What is the simplified form of x squared plus 6 times x plus 8 all over 4 minus x squared.?


a. negative times the quantity x plus 2 all over 4 plus x.
b. negative times the quantity x minus 2 all over 4 minus x.
c. x plus 4 all over 4 minus x.
d. negative times the quantity x plus 4 all over x minus 2.

Answer 1

\[x ^{2}+6x + 8 / 4-x ^{2}\]

Answer 2

Is that right, for the non-simplified version?

Answer 3

Yes

Answer 4

We just have to factor the quadratic in the numerator, and the difference of squares in the denominator.

Answer 5

\[\frac{ x^2 +6x + 8 }{ 4 - x^2 }\]
Factoring out
:\[x^2 + 6x + 8 => x^2 + 4x + 2x + 8 => x(x+4) +2(x+ 4) => x(x+4)(x+2)\]
\[\frac{ (x+4)(x+2) }{ (x+4) } = (x+2)\]

Answer 6

So, x^2+6x+8 becomes (x+4)(x+2)
and 4-x^2 becomes (2-x)(2+x)

Answer 7

@RedNeckOutLaw

Answer 8

Then we cancel out the common factor of (x+4), leaving us with (x+2)

Answer 9

Cos, wouldnt it be (x+2) (x+2)

Answer 10

No. A difference of squares will always yield a + and - sign.

Answer 11

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

x^2-9 = (x+3)(x-3)

etc.

Answer 12

Ohhh, i understand where yoru comignfrom

Answer 13

Remember, when it's 2 squares, like x^2 and a 3, 9, 16, 25, 36, etc. and you are taking the difference,

Example, x^2-9 or 9-x^2
x^2-25 or 25-x^2

It has to be be (x+3)(x-3) or (3+x)(3-x)
(x+5)(x-5) or (5+x)(5-x)

Where it has to be a + times a -, to give a negative.

Answer 14

=)

Answer 15

So fir the first example it can either way. so f its x^2-25 or 25-x^2. its (x+5)(x-5) or (5+x)(5-x) its because 5x5 is 25

Answer 16

@Cosmichaotic

Answer 17

Exactly, yes.

Answer 18

Ok, so whats the next thing we do?

Answer 19

Well, in your problem, it becomes