What is the answer to (si)/(P(x))=(x-1)^2+x-1 ?

The answer to (si)/(P(x))=(x-1)^2+x-1 is

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(si)/(P(x))=(x-1)^2+x-1

\frac{s i}{P ( x )} = (x - 1)^{2} + x - 1

s = 0, s = 0, s = 0, x = 0, x \in R, x = 1, P \in R P = 0 P \in R

Solution steps

\frac{s i}{P ( x )} = (x - 1)^{2} + x - 1

Multiply both sides by

P (x)

\frac{s i}{P ( x )} P (x) = (x - 1)^{2} P (x) + x P (x) - 1 \cdot P (x)

Expand

i s = x^{2} P (x) - x P (x)

Rewrite

i s

in standard complex form:

0 + s i

0 + s i = x^{2} P (x) - x P (x)

Rewrite

x^{2} P (x) - x P (x)

in standard complex form:

(x^{2} P (x) - x P (x)) + 0 i

0 + s i = (x^{2} P (x) - x P (x)) + 0 i

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[0 = x^{2} P (x) - x P (x) s = 0]

[0 = x^{2} P (x) - x P (x) s = 0] : s = 0, s = 0, s = 0, x = 0, x \in R, x = 1, P \in R P = 0 P \in R

s = 0, s = 0, s = 0, x = 0, x \in R, x = 1, P \in R P = 0 P \in R

(z - \frac{3}{5})^{2} + (5 i)^{2} = 0

- i = x^{2} - y^{2} + 2 x y i

i x^{2} - 4 x - 4 i = 0

(x + i y) (3 + 4 i) = 3 - 4 i

x + 1 + i (y + 1) = 2

What is the answer to (si)/(P(x))=(x-1)^2+x-1 ?
The answer to (si)/(P(x))=(x-1)^2+x-1 is