What is (a+2+7/(a-5))(a-2-5/(a+2)) ?

The solution to (a+2+7/(a-5))(a-2-5/(a+2)) is ((a^2-3a-3)(a^2-9))/((a+2)(a-5))

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simplify (a+2+7/(a-5))(a-2-5/(a+2))

simplify

(a + 2 + \frac{7}{a - 5}) (a - 2 - \frac{5}{a + 2})

\frac{( a ^{2} - 3 a - 3 ) ( a ^{2} - 9 )}{( a + 2 ) ( a - 5 )}

Solution steps

(a + 2 + \frac{7}{a - 5}) (a - 2 - \frac{5}{a + 2})

Join

a + 2 + \frac{7}{a - 5} : \frac{a ^{2} - 3 a - 3}{a - 5}

= \frac{a ^{2} - 3 a - 3}{a - 5} (a - 2 - \frac{5}{a + 2})

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( a ^{2} - 3 a - 3 ) ( a - 2 - \frac{5}{a + 2} )}{a - 5}

Simplify

(a^{2} - 3 a - 3) (a - 2 - \frac{5}{a + 2}) : \frac{( a ^{2} - 3 a - 3 ) ( a ^{2} - 9 )}{a + 2}

= \frac{\frac{( a ^{2} - 3 a - 3 ) ( a ^{2} - 9 )}{a + 2}}{a - 5}

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{( a ^{2} - 3 a - 3 ) ( a ^{2} - 9 )}{( a + 2 ) ( a - 5 )}

(a + b)^{3}

\frac{x ^{2} + 2 x - 1}{( x + 1 ) ^{2}}

\frac{2}{( n + 1 ) ( n + 3 )}

(1 + \frac{x}{2})^{8}

(6 x - i)^{2}

What is (a+2+7/(a-5))(a-2-5/(a+2)) ?
The solution to (a+2+7/(a-5))(a-2-5/(a+2)) is ((a^2-3a-3)(a^2-9))/((a+2)(a-5))