Simplify:

$\frac{4 + 5}{4 - 5} + \frac{4 - 5}{4 + 5}$

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Theodore Discussed

Simplify:

\frac{4 + 5}{4 - 5} + \frac{4 - 5}{4 + 5}

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Text solutionVerified

\frac{( 4 + 5 ) \times ( 4 + 5 )}{( 4 - 5 ) \times ( 4 + 5 )} + \frac{( 4 - 5 ) \times ( 4 - 5 )}{( 4 + 5 ) \times ( 4 - 5 )}

\Rightarrow \frac{( 4 + 5 ) ^{2}}{( 16 - 5 )} + \frac{( 4 - 5 ) ^{2}}{( 16 - 5 )}

[ Applying

(a^{2} - b^{2}) = (a + b) (a - b)

]

\Rightarrow \frac{( 16 + 5 + 8 5 + 16 + 5 - 8 5 )}{11}

\Rightarrow \frac{42}{11}

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