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

Assessment: JAMB UTME - Mathematics - 1984 Subject: General Mathematics

Question 1 Report

\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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If \(a = \frac{2x}{1-x}\) and \(b = \frac{1+x}{1-x}\), then \(a^2 - b^2\) in the simplest form is \(\frac{3x+1}{1-x}\)

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