Question

1-x/1+x=2x+1/-2x+5 find x

Answer 1

x =
`(2)/(5)`

Explanation:

Given

`(1-x)/(1+x)` =
`(2x+1)/(-2x+5)` ( cross- multiply )

(2x + 1)(1 + x) = (1 - x)(- 2x + 5) ← expand parenthesis on both sides using FOIL

2x + 2x² + 1 + x = - 2x + 5 + 2x² - 5x , simplify

2x² + 3x + 1 = 2x² - 7x + 5 ( subtract 2x² from both sides )

3x + 1 = - 7x + 5 ( add 7x to both sides )

10x + 1 = 5 ( subtract 1 from both sides )

10x = 4 ( divide both sides by 10 )

x =
`(4)/(10)` =
`(2)/(5)`

Answer 2

x = 2/5

Explanation:

`(1-x)/(1+x)=(2x+1)/(-2x+5)`

Cross multiply,

(1 - x)(-2x + 5) = (2x +1)(1 + x)

Use FOIL method to multiply,

1*(-2x) + 1*5 - 2x *(-x) + 5*(-x) =2x *1 + 2x *x + 1*1 + 1*x

-2x + 5 + 2x² -5x = 2x + 2x² + 1 + x

Combine like terms,

-2x - 5x + 2x² + 5 = 2x² + 2x +x + 1

-7x + 2x² + 5 = 2x² + 3x + 1

-7x + 2x² - 2x² - 3x = 1 - 5

-7x - 3x = - 4

-10x = -4

x = -4/-10

x = 2/5