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

The solution to 1/(a-5)+a/(a^2-4a-5)+(a+5)/(a^2+2a+1) is (3a^2+3a-24)/((a-5)(a+1)^2)

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

simplify

\frac{1}{a - 5} + \frac{a}{a ^{2} - 4 a - 5} + \frac{a + 5}{a ^{2} + 2 a + 1}

\frac{3 a ^{2} + 3 a - 24}{( a - 5 ) ( a + 1 ) ^{2}}

Solution steps

\frac{1}{a - 5} + \frac{a}{a ^{2} - 4 a - 5} + \frac{a + 5}{a ^{2} + 2 a + 1}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(a + 1)^{2} + a (a + 1) + (a + 5) (a - 5) : 3 a^{2} + 3 a - 24

= \frac{3 a ^{2} + 3 a - 24}{( a - 5 ) ( a + 1 ) ^{2}}

(3 a - 2 b)^{3}

\frac{16}{28}

(3 - x^{2})^{2}

\frac{x ^{2} - x - 12}{x + 3}

3 (x - 4)^{2}

What is 1/(a-5)+a/(a^2-4a-5)+(a+5)/(a^2+2a+1) ?
The solution to 1/(a-5)+a/(a^2-4a-5)+(a+5)/(a^2+2a+1) is (3a^2+3a-24)/((a-5)(a+1)^2)