Wykonaj działania, odpowiedź podaj ...- Zadanie 5: MATeMAtyka 2. Zakres podstawowy i rozszerzony

Rozwiązanie

$a)$

Zał:

$a^{2} b^{2} \neq = 0, a - b \neq = 0, a + b \neq = 0$

$a \neq = 0, b \neq = 0, a \neq = b, a \neq = - b$

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

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

$b)$

Zał:

$a - 1 \neq = 0, a^{2} \neq = 0, b \neq = 0, b - a b \neq = 0$

$a \neq = 1, a \neq = 0, b \neq = 0, b (1 - a) \neq = 0$

$a \neq = 1, a \neq = 0, b \neq = 0$

$(a - \frac{a ^{2}}{a - 1})^{- 1} (\frac{a + 1}{b} - \frac{1}{b - a b}) = (\frac{a ( a - 1 )}{a - 1} - \frac{a ^{2}}{a - 1})^{- 1} (\frac{a + 1}{b} - \frac{1}{b ( 1 - a )}) =$

$= (\frac{a ^{2} - a - a ^{2}}{a - 1})^{- 1} (\frac{( a + 1 ) ( 1 - a )}{b ( 1 - a )} - \frac{1}{b ( 1 - a )}) = (\frac{- a}{a - 1})^{- 1} (\frac{a - a ^{2} + 1 - a - 1}{b ( 1 - a )}) =$