Question

Multiply. Assume that all expressions are defined.
\[\frac{ x ^{2}-16 }{ x ^{2}-4x+4 } \times \frac{ x-2 }{ x ^{2}+6x+8 }\]

Answer 1

ok x^2 -16
can be simplified into (x-4)(x+4)
using (a+b)(a-b) = a^2 -b^2

x^2-4x+4 = (x-2)^2
using (a-b)^2 = a^2 -2ab+b^2

x^2+6x+8 = x^2 + 4x +2x + 8 = x(x+4)+2(x+4) = (x+2)(x+4)

now we have so far :

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

Answer 2

can you do it now ?

Answer 3

:/ no

Answer 4

ok you see we have x+4 in the denominator and in the numerator so we can eliminate
smae with (x-2) and (x-2)^2 we will left with x-2 in the denominator

Answer 5

(x-4)/(x-2)(x+2)

Answer 6

so its x-4/x+2

Answer 7

no i wrote you the final answer in the drawing

Answer 8

there is (x-2) in the denominator
since it was squared and on the numerator it was to the power of one
so there is one left in the denominator..

Answer 9

okay thank you!!!

Answer 10

if a = x-2 so its like :
\[\frac{ a }{ a^2 } = \frac{ 1 }{ a }\]

Answer 11

yw