Question

2. Divide the following and write your answer in lowest terms

Answer 1

Given, $\bold{\frac{x}{x+1}\div\frac{x^2}{x^2-1}}$,
we know,
a² - b² = (a - b)(a + b) ,from algebraic identities
∴ x² - 1 = (x - 1)(x + 1)

Now, $\bold{\frac{x}{x+1}\div\frac{x^2}{(x-1)(x+1)}}$
$= \bold{\frac{\frac{x}{x+1}}{\frac{x^2}{(x-1)(x+1)}}}\\\\=\bold{\frac{x(x-1)(x+1)}{(x+1)x^2}}\\=\bold{\frac{x-1}{x}}$

Hence, answer is (x - 1)/x

Answer 2

Solution :

x/( x + 1 ) ÷ x²/( x² - 1 )

= x/( x + 1 ) × ( x² - 1² )/x²

= [ x ( x + 1 )( x - 1 )/[ (x+1)x²]

[ Since , a² - b² = (a + b)(a - b)]

After cancellation , we get

= ( x - 1 )/x

Or

= x/x - 1/x

= 1 - 1/x

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