(x^2 - 1 / x + 3) is divided by (x^2 + 4x + 3 / x - 7 )?

Question

Please solve this division for me .

Answer 1

factorize
(x^2 - 1 / x + 3) * (x-7) / (x^2 + 4x + 3)
= (x+1)*(x-1) / (x+3) * (x-7) / [ (x+3)*(x+1)]
= (x-1)*(x-7) / (x+3)^2

Answer 2

You simply plug a value into x and get the result:

for the first phrase (plug 2 for x):

(x^2 - 1) / (x+3)
4 - 1 / 2 + 3
3 / 5


For the next phrase (plus 2 for x again)

(x^2 + 4x + 3) / (x - 7)
4 + 8 + 3 / 2 - 7
15 / -5

Now to see if they are divisible:

(3 / 5) / (15 / -5) = (3*-5) / (5*15) = -15 / 75 = -1/5

Since all the powers and exponents are 2 and they are even, if you plug negative values for x you will get the same result.

Good luck.

Answer 3

N = (x - 1).(x + 1) / (x + 3)
D = (x + 3).(x + 1) / (x - 7)

N / D = (x - 1).(x - 7) / (x + 3)²

Answer 4

Given that x does not equal -3 or 7

[(x - 1)(x - 7)] / (x + 3)^2

Answer 5

(x-1)(x-7)/(x+3)^2