Simplify (x+1)/(x^2-x-20)-(x+4)/(x^2-4x-5)+(x+5)/(x^2+5x+4)

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -20}$ and whose sum is ${\displaystyle -1}$.

Write the factored form using these integers.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -5}$ and whose sum is ${\displaystyle -4}$.

Write the factored form using these integers.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle 4}$ and whose sum is ${\displaystyle 5}$.

Write the factored form using these integers.

Expand ${\displaystyle (x+1)(x+1)}$ using the FOIL Method.

Simplify and combine like terms.

Apply the distributive property.

Multiply ${\displaystyle -1}$ by ${\displaystyle 4}$.

Expand ${\displaystyle (-x-4)(x+4)}$ using the FOIL Method.

Simplify and combine like terms.

Expand ${\displaystyle (x+5)(x-5)}$ using the FOIL Method.

Combine the opposite terms in ${\displaystyle x\cdot x+x\cdot -5+5x+5\cdot -5}$.

Simplify each term.

Combine the opposite terms in ${\displaystyle x^2+2x+1-x^2-8x-16+x^2-25}$.

Subtract ${\displaystyle 8x}$ from ${\displaystyle 2x}$.

Simplify the expression.