What is (a-5)(a+1)(1+(3a-37)/(a^2-4a-5)) ?

The solution to (a-5)(a+1)(1+(3a-37)/(a^2-4a-5)) is a^2-a-42

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simplify (a-5)(a+1)(1+(3a-37)/(a^2-4a-5))

simplify

(a - 5) (a + 1) (1 + \frac{3 a - 37}{a ^{2} - 4 a - 5})

a^{2} - a - 42

Solution steps

(a - 5) (a + 1) (1 + \frac{3 a - 37}{a ^{2} - 4 a - 5})

Join

1 + \frac{3 a - 37}{a ^{2} - 4 a - 5} : \frac{a ^{2} - a - 42}{a ^{2} - 4 a - 5}

= (a - 5) (a + 1) \frac{a ^{2} - a - 42}{a ^{2} - 4 a - 5}

Apply the fraction rule:

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

= \frac{( a - 5 ) ( a + 1 ) ( a ^{2} - a - 42 )}{a ^{2} - 4 a - 5}

Factor

a^{2} - 4 a - 5 : (a + 1) (a - 5)

= \frac{( a - 5 ) ( a + 1 ) ( a ^{2} - a - 42 )}{( a + 1 ) ( a - 5 )}

Cancel the common factor:

a - 5

= \frac{( a + 1 ) ( a ^{2} - a - 42 )}{a + 1}

Cancel the common factor:

a + 1

= a^{2} - a - 42

(z + 1 + 4 i)^{2}

x^{2} d x (x - 4)

(1 - \frac{207}{n}) (1 - \frac{207}{n - 414})

(x - c) (x + c)

\frac{X - 3}{( X + 2 ) ( X + 1 ) ^{2}}

What is (a-5)(a+1)(1+(3a-37)/(a^2-4a-5)) ?
The solution to (a-5)(a+1)(1+(3a-37)/(a^2-4a-5)) is a^2-a-42