Factorise and simplify x²-8x+16 ÷ 16-x²?

👨🏻‍🏫 學術台 數學
2008-12-20 1:27 pm
Hi,

I need some help with this one, I almost got it right but not quiet.

x²-8x+16 ÷ 16-x²

Thanks
David
更新1:

Just need some clarification on one part. The formula so far is: x² - 8x + 16 ÷ 16 - x² (x - 4)(x - 4) ÷ (4 - x)(4 + x) (x - 4)(x - 4) ÷ -(x - 4)(4 + x) When the (x-4) is canceled on each side of the equasion what happens to the - or does that disappear with the (x-4)? -(x - 4) ÷ (4 + x) (4 - x)/(4 + x)

回答 (11)

2008-12-20 1:46 pm
✔ 最佳答案
Hi!!

Let's do it:

(x² - 8x + 16) / (16 - x²)

The first one is a trinomial perfect square of a difference.
The second one is a sum times a difference.

So, let's factorise them:

((x)² - 2(x ∙ 4) + 4²) / ((4 + x)(4 - x)) =
(x - 4)²/((4 + x)(4 - x)) =
((x - 4)(x - 4))/((4 + x)(4 - x)) =

If you notice, 4 - x is equal to -(x - 4) , so it's quotient yields -1.

(x - 4)/(4 + x) ∙ (x - 4)/(4 - x) =
(x - 4)/(4 + x) ∙ (-1) =
(4 - x)/(4 + x)

And that's the final answer =D.

∴ (4 - x)/(4 + x)

Bye hope it helped!!
參考: Self-Knowledge
👍 0 👎 0
2016-04-11 7:38 am
(X-4)^2/(4-X)(4+X)=(X-4)/-(4+X)=
(4-X)/(4+X)
👍 0 👎 0
2008-12-20 2:28 pm
a^2 - b^2 = (a + b)(a - b)

(x^2 - 8x + 16)/(16 - x^2)
= (x^2 - 4x - 4x + 16)/(4^2 - x^2)
= [(x^2 - 4x) - (4x - 16)]/(4 + x)(4 - x)
= [x(x - 4) - 4(x - 4)]/(4 + x)(4 - x)
= (x - 4)(x - 4)/(4 + x)(4 - x)
= -(-x + 4)(x - 4)/(x + 4)(4 - x)
= -(4 - x)(x - 4)/(x + 4)(4 - x)
= -(x - 4)/(x + 4)
👍 0 👎 0
2008-12-20 2:05 pm
(x-4)^2/(4-x)^2=(x-4)^2/(4-x)(4+x)=
=-(4-x)(4+x)/(4-x)(4+x)=-1
👍 0 👎 0
2008-12-20 2:00 pm
x² - 8x + 16 ÷ 16 - x²
(x - 4)(x - 4) ÷ (4 - x)(4 + x)
(x - 4)(x - 4) ÷ -(x - 4)(4 + x)
-(x - 4) ÷ (4 + x)
(4 - x)/(4 + x)
👍 0 👎 0
2008-12-20 1:46 pm
x²-8x+16 ÷ 16-x² can be written as

x²-8x+16 / 16-x²

x²-8x+16 / (4)²-x² 4² = 16

x²-4x-4x+16 / (4)²-x² splitting -8x

x(x-4) - 4(x-4) / (4)²-x²

(x-4)² / (4-x)(4+x)

- (x-4)² / (x-4)(4+x) we change the denominator sign


- (x-4) / (4+x)

is the answer
👍 0 👎 0
2008-12-20 1:33 pm
(x²-8x+16 )/( 16-x²) = (x -4)(x-4) /[(x+4)(x-4)] = (x-4)/(x+4)
👍 0 👎 0
2008-12-20 1:33 pm
(x²-8x+16) ÷ (16-x²)
= - (x-4)²/(x-4)(x+4) = (4-x)/(4+x) ; if x ≠ 4
👍 0 👎 0
2008-12-20 1:33 pm
x²-8x+16 = (x-4).(x-4)

16 - x² = -1.(x-4).(x+4)

x²-8x+16 ÷ 16-x² = (x-4) / -1.(x+4)
= -1.(4-x) / -1. (x+4) [ -1 cancel each other ]
= (4-x) (x+4)
參考: hope this help ^_^
👍 0 👎 0
2008-12-20 1:32 pm
-8x+1
👍 0 👎 0


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