Question

Can somebody explain this?

Answer 1

`(2 x - 1 + y )/(2x + y + 1)`

Explanation:

In the expression:

`\frac{4 {x}^(2) - {y}^(2) - 4x + 1 }{4 {x}^(2) - {y}^(2) - 2y - 1 }`

Reorder the terms

`⟹\frac{(4 {x}^(2) - 4x + 1) - {y}^(2) }{4 {x}^(2) - {y}^(2) - 2y - 1 }`

Rewrite the expression

`⟹ \frac{(2x {)}^(2) - 2 * 2x + {1}^(2) - {y}^(2) }{ {4x}^(2) - {y}^(2) - 2y - 1 }`

Factor the expression

`⟹ \frac{(2x - 1 {)}^(2) - {y}^(2) }{4 {x}^(2) - {y}^(2) - 2y - 1 }`

`⟹ \frac{((2x - 1) + y)((2x - 1) - y)}{4 {x}^(2) - {y}^(2) - 2y - 1}`

Reorder terms

`\frac{((2x - 1) + y)((2x - 1) - y)}{ {4x}^(2) + ( - {y}^(2) - 2y - 1}`

Factor greatest common factors out

`\frac{((2x - 1) + y)((2x - 1) - y)}{ {4x}^(2) - ( {y}^(2) + 2y + 1) }`

Rewrite the expression

`\frac{((2x - 1) + y)((2x - 1) - y)}{ {4x}^(2) - ( {y}^(2) + 2y + {1}^(2)) }`

Factor the expression

`\frac{((2x - 1) + y)((2x - 1) - y)}{ {4x }^(2) - (y + 1)}`

I'm sorry for breaking but it's a very long explanation

Answer 2

2x-1+y

---------- (meant to be a fraction line)

2x+y+1