Question

Am nevoie de ajutot ​

Answer 1

Răspuns:

• $\boxed{\bf{c) \: \frac{1}{a} }}$
• $\boxed{\bf{d) a - b}}$

Explicație pas cu pas:

$\bf{c) \: ( \frac{a}{a - 1} + \frac{1}{a + 1} + \frac{2}{ {a}^{2} - 1} - \frac{2a}{(a - 1)(a + 1)} ) \div \frac{a {}^{3 } + a}{ {a}^{2} - 1 } }$

$\bf{( \frac{a}{a - 1} + \frac{1}{a + 1} + \frac{2}{(a - 1)(a + 1)} - \frac{2a}{(a - 1)(a + 1)}) \times \frac{a {}^{2} - 1 }{a {}^{3} + a } }$

$\bf{( \frac{a \times (a + 1) + a - 1 + 2}{(a - 1)(a + 1)} - \frac{2a}{(a - 1)(a + 1)} ) \times \frac{(a - 1)(a + 1)}{a(a { }^{2} + 1) } }$

$\bf{( \frac{a {}^{2} + 2a + 1 }{(a - 1)(a + 1)} - \frac{2a}{(a - 1)(a + 1)} ) \times \frac{(a - 1)(a + 1)}{a(a {}^{2} + 1) } }$

$\bf{( \frac{(a + 1) {}^{2} }{(a - 1)(a + 1)} - \frac{2a}{(a - 1)(a + 1)} ) \times \frac{(a - 1)(a + 1)}{a(a {}^{2} + 1) } }$

$\bf{( \frac{(a + 1) {}^{2} }{(a - 1)(a + 1)} - \frac{2a}{(a - 1)(a + 1)} ) \times \frac{(a - 1)(a + 1)}{a( {a}^{2} + 1)} }$

$\bf{( \frac{a + 1}{a - 1} - \frac{2a}{(a - 1)(a + 1)} ) \times \frac{(a - 1)(a + 1)}{a(a {}^{2} + 1) } }$

$\bf{ \frac{(a + 1) {}^{2} - 2a}{(a - 1)(a + 1)} \times \frac{(a - 1)(a + 1)}{a(a {}^{2} + 1)} }$

$\bf{ \frac{a {}^{2} + 2a + 1 - 2a }{a + 1} \times \frac{a + 1}{a(a {}^{2} + 1) } }$

$\bf{ \frac{a {}^{2} + 1 }{a + 1} \times \frac{a + 1}{a(a {}^{2} + 1) } = \:\boxed{\bf{ \frac{1}{a} }}}$

$\bf{d) \: (a - \frac{4ab}{a + b} + b) \div ( \frac{a}{a + b} - \frac{b}{b - a} - \frac{2ab}{a {}^{2} - b {}^{2} } ) }$

$\bf{ \frac{a(a + b) - 4ab + b(a + b)}{a + b} \div ( \frac{a}{a + b} - \frac{b}{ - (a - b)} - \frac{2ab}{(a - b)(a + b)} )}$

$\bf{ \frac{a {}^{2} + ab - 4ab + ab + b {}^{2} }{a + b} \div ( \frac{a}{a + b} + \frac{b}{a - b} - \frac{2ab}{(a - b)(a + b)} )}$

$\bf{ \frac{a {}^{2} - 2ab + b {}^{2} }{a + b} \div \frac{a(a - b) + b(a + b) - 2ab}{(a - b)(a + b)} }$

$\bf{ \frac{(a - b) {}^{2} }{a + b} \div \frac{a {}^{2} - ab + ab + b {}^{2} - 2ab}{(a - b)(a + b)} }$

$\bf{ \frac{(a - b) {}^{2} }{a + b} \div \frac{a {}^{2} - 2ab + b {}^{2} }{(a - b)(a + b)} }$

$\bf{ \frac{(a - b) {}^{2} }{a + b} \div \frac{(a - b) {}^{2} }{(a - b)(a + b)} = \frac{(a - b) {}^{2} }{a + b} \div \frac{a - b}{a + b} }$

$\bf{ \frac{(a - b) {}^{2} }{a + b} \times \frac{a + b}{a - b} = \boxed{\bf{a - b}}}$

Bafta ! :)