Question

(x-1)(x+3)=(x+1)^2+x​

Answer 1

Ответ:

(x - 1)(x + 3) = (x + 1)^2 + x

​ х^2 + 3х - х -  3 = х^2 + 2х + 1 + х

3х - х - 3 = 2х + 1 + х

2х - 3 = 3х + 1

2х - 3х = 1 + 3

х = -4

Answer 2

Let's expand and simplify the equation:

$(x-1)(x+3) = (x+1)^2 + x$

First, expand the left side:

$(x-1)(x+3) = x(x+3) - 1(x+3)$

$= x^2 + 3x - x - 3$

Combine like terms:

$= x^2 + 2x - 3$

Now, compare it to the right side of the equation:

$(x+1)^2 + x$

Expand $(x+1)^2$:

$(x+1)(x+1) = x^2 + 2x + 1$

Now, add $x$:

$x^2 + 2x + 1 + x$

Combine like terms:

$x^2 + 3x + 1$

So, the equation becomes:

$x^2 + 2x - 3 = x^2 + 3x + 1$

Now, subtract $x^2$ from both sides to simplify:

$2x - 3 = 3x + 1$

Subtract $2x$ from both sides:

$-3 = x + 1$

Subtract 1 from both sides:

$-4 = x$

Therefore, the solution to the equation is $x = -4$.