Question

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

Answer 1

Answer:

 x = 2/5

Step-by-step explanation:

$\frac{1-x}{1+x}=\frac{2x+1}{-2x+5}$

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

Answer 2

Answer:

x = $\frac{2}{5}$

Step-by-step explanation:

Given

$\frac{1-x}{1+x}$ = $\frac{2x+1}{-2x+5}$ ( 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 = $\frac{4}{10}$ = $\frac{2}{5}$