If a = 2x1−x 2 x 1 − x and b = 1+x1−x 1 + x 1 − x , then a2 - b2 in the simplest form is

Question 1 Report

If a = $\frac{2 x}{1 - x}$ and b = $\frac{1 + x}{1 - x}$ , then a2 - b2 in the simplest form is $\frac{3 x + 1}{1 - x}$

\frac{3 x + 1}{1 - x}

3x²−1

(x−1)²

3x−2

x−1

3x−2

1−X

3x²−1

(x−1)

Answer Details

a2 - b2 = ( $\frac{2 x}{1 - x}$ )2 - ( $\frac{1 + x}{1 - x}$ )2
= ( $\frac{2 x}{1 - x} + \frac{1 + x}{1 - x}$ )( $\frac{2 x}{1 - x} - \frac{1 + x}{1 - X}$ )
= ( $\frac{3 x + 1}{1 - x}$ )( $\frac{x - 1}{1 - x}$ )
= $\frac{3 x + 1}{x - 1}$

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Linear Inequalities

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