[tex] \frac{ \frac{1}{a} - \frac{1}{b} }{ \frac{1}{b} {}^{2} - \frac{1}{a} { \\ }^{2} } \\ = - \frac{ - ( \frac{1}{b} - \frac{1}{a} ) }{ (\frac{1}{b} \times \frac{1}{a}) \times( \frac{1}{b} \times \frac{1}{a}) } \\ = \frac{ - 1}{ \frac{a + b}{ab} } \\ = - \frac{ab}{a + b} [/tex]
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Aljabar
[tex] \frac{ \frac{1}{a} - \frac{1}{b} }{ \frac{1}{ {b}^{2} } - \frac{1}{ {a}^{2} } } \\ \frac{ \frac{b - a}{ab} }{ \frac{ {a}^{2} - {b}^{2} }{ {a}^{2} {b}^{2} } } \\ \frac{b - a}{ab} . \frac{ {a}^{2} {b}^{2} }{ {a}^{2} - {b}^{2} } \\ \frac{ - (a - b)}{ab} . \frac{( {ab})^{2} }{(a + b)(a - b)} \\ \frac{ - (ab) {}^{2 - 1} }{(a + b)} = \frac{ - (ab)}{(a + b)} = \frac{ - ab}{a + b} [/tex]
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[tex] \frac{ \frac{1}{a} - \frac{1}{b} }{ \frac{1}{b} {}^{2} - \frac{1}{a} { \\ }^{2} } \\ = - \frac{ - ( \frac{1}{b} - \frac{1}{a} ) }{ (\frac{1}{b} \times \frac{1}{a}) \times( \frac{1}{b} \times \frac{1}{a}) } \\ = \frac{ - 1}{ \frac{a + b}{ab} } \\ = - \frac{ab}{a + b} [/tex]
Penjelasan dengan langkah-langkah:
Aljabar
[tex] \frac{ \frac{1}{a} - \frac{1}{b} }{ \frac{1}{ {b}^{2} } - \frac{1}{ {a}^{2} } } \\ \frac{ \frac{b - a}{ab} }{ \frac{ {a}^{2} - {b}^{2} }{ {a}^{2} {b}^{2} } } \\ \frac{b - a}{ab} . \frac{ {a}^{2} {b}^{2} }{ {a}^{2} - {b}^{2} } \\ \frac{ - (a - b)}{ab} . \frac{( {ab})^{2} }{(a + b)(a - b)} \\ \frac{ - (ab) {}^{2 - 1} }{(a + b)} = \frac{ - (ab)}{(a + b)} = \frac{ - ab}{a + b} [/tex]
Semoga membantu