Answer:
x = [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1-x}{1+x}[/tex] = [tex]\frac{2x+1}{-2x+5}[/tex] ( 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 = [tex]\frac{4}{10}[/tex] = [tex]\frac{2}{5}[/tex]
Answer:
x = 2/5
Step-by-step explanation:
[tex]\frac{1-x}{1+x}=\frac{2x+1}{-2x+5}[/tex]
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
