Question

Helppp!!Simplify:-1...a/a-b - b/a+b - 2ab/b²-a²2...1/a-3 - 1/a-1 + 1/a+3 - 1/a+1​

Answer 1

Answer:

#1

$GIVEN;$

$\displaystyle{ \frac{a}{a - b} - \frac{b}{a + b} - \frac{2ab}{ {b}^{2} - {a}^{2} } }$

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

$\displaystyle{ \frac{ {a}^{2} + ab - ab + {b}^{2} }{ {a}^{2} - {b}^{2} } + \frac{2ab}{ {a}^{2} - {b}^{2} } }$

$\displaystyle{ \frac{ {(a + b)}^{2} }{(a + b)(a - b)} }$

$\displaystyle{ \frac{ {(a + b)(a + b)} }{(a + b)(a - b)} }$

$\displaystyle{ \frac{a + b}{a - b} }$

#2

$GIVEN;$

$\displaystyle{ \frac{1}{a - 3} - \frac{1}{a - 1} + \frac{1}{a + 3} - \frac{1}{a + 1} }$

$\displaystyle{ \frac{1}{a - 3} + \frac{1}{a + 3} - \frac{1}{a - 1} - \frac{1}{a + 1} }$

$\displaystyle{ \frac{a + 3 + a - 3}{(a + 3)(a - 3)} - \left( \frac{1}{a - 1} + \frac{1}{a + 1} \right) }$

$\displaystyle{ \frac{2a}{ {a}^{2} - {3}^{2} } - \frac{a + 1 + a - 1}{ {a}^{2} - {1}^{2} } }$

$\displaystyle{ \frac{2a}{ {a}^{2} - 9} - \frac{2a}{ {a}^{2} - 1 } }$

$\displaystyle{ \frac{2a( {a}^{2} - 1) - 2a( {a}^{2} - 9) }{( {a}^{2} - 1)( {a}^{2} - 9)} }$

$\displaystyle{ \frac{ {2a}^{3} - 2a - {2a}^{3} + 18a }{( {a}^{2} - 1)( {a}^{2} - 9)} }$

$\displaystyle{ \frac{16a}{( {a}^{2} - 1)( {a}^{2} - 9) } }$

Step-by-step explanation:

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