`(x+3)/(x^2-25) - (x-1)/(x-5) + 3/(x+3)` Perform the indicated operation(s) and simplify

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`(x+3)/(x^2-25)-(x-1)/(x-5)+3/(x+3)`

Factorize the denominator of the first term by using the identity: `a^2-b^2=(a+b)(a-b)`

`=(x+3)/((x+5)(x-5))-(x-1)/(x-5)+3/(x+3)`

LCD of the above expression is`(x+5)(x-5)(x+3)`

`=((x+3)(x+3)-(x+5)(x+3)(x-1)+3(x+5)(x-5))/((x+5)(x-5)(x+3))`

expand the terms in the numerator and combine the like terms to simplify,

`=((x^2+6x+9)-(x^2+3x+5x+15)(x-1)+3(x^2-25))/((x+5)(x-5)(x+3))`

`=((x^2+6x+9)-(x^2+8x+15)(x-1)+3(x^2-25))/((x+5)(x-5)(x+3))`

`=((x^2+6x+9)-(x^3+8x^2+15x-x^2-8x-15)+3(x^2-25))/((x+5)(x-5)(x+3))`

`=((x^2+6x+9)-(x^3+7x^2+7x-15)+(3x^2-75))/((x+5)(x-5)(x+3))`

`=(x^2+6x+9-x^3-7x^2-7x+15+3x^2-75)/((x+5)(x-5)(x+3))`

`=(-x^3+x^2-7x^2+3x^2+6x-7x+9+15-75)/((x+5)(x-5)(x+3))`

`=(-x^3-3x^2-x-51)/((x+5)(x-5)(x+3))`

`=(-(x^3+3x^2+x+51))/((x+5)(x-5)(x+3))`

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`(x+3)/(x^2-25)-(x-1)/(x-5)+3/(x+3)`

Factorize the denominator of the first term by using the identity: `a^2-b^2=(a+b)(a-b)`

`=(x+3)/((x+5)(x-5))-(x-1)/(x-5)+3/(x+3)`

LCD of the above expression is`(x+5)(x-5)(x+3)`

`=((x+3)(x+3)-(x+5)(x+3)(x-1)+3(x+5)(x-5))/((x+5)(x-5)(x+3))`

expand the terms in the numerator and combine the like terms to simplify,

`=((x^2+6x+9)-(x^2+3x+5x+15)(x-1)+3(x^2-25))/((x+5)(x-5)(x+3))`

`=((x^2+6x+9)-(x^2+8x+15)(x-1)+3(x^2-25))/((x+5)(x-5)(x+3))`

`=((x^2+6x+9)-(x^3+8x^2+15x-x^2-8x-15)+3(x^2-25))/((x+5)(x-5)(x+3))`

`=((x^2+6x+9)-(x^3+7x^2+7x-15)+(3x^2-75))/((x+5)(x-5)(x+3))`

`=(x^2+6x+9-x^3-7x^2-7x+15+3x^2-75)/((x+5)(x-5)(x+3))`

`=(-x^3+x^2-7x^2+3x^2+6x-7x+9+15-75)/((x+5)(x-5)(x+3))`

`=(-x^3-3x^2-x-51)/((x+5)(x-5)(x+3))`

`=(-(x^3+3x^2+x+51))/((x+5)(x-5)(x+3))`

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