# Simplify 5/(x+5)+3/(x-5)

5x+5+3x-5
To write 5x+5 as a fraction with a common denominator, multiply by x-5x-5.
5x+5⋅x-5x-5+3x-5
To write 3x-5 as a fraction with a common denominator, multiply by x+5x+5.
5x+5⋅x-5x-5+3x-5⋅x+5x+5
Write each expression with a common denominator of (x+5)(x-5), by multiplying each by an appropriate factor of 1.
Multiply 5x+5 and x-5x-5.
5(x-5)(x+5)(x-5)+3x-5⋅x+5x+5
Multiply 3x-5 and x+5x+5.
5(x-5)(x+5)(x-5)+3(x+5)(x-5)(x+5)
Reorder the factors of (x-5)(x+5).
5(x-5)(x+5)(x-5)+3(x+5)(x+5)(x-5)
5(x-5)(x+5)(x-5)+3(x+5)(x+5)(x-5)
Combine the numerators over the common denominator.
5(x-5)+3(x+5)(x+5)(x-5)
Simplify the numerator.
Apply the distributive property.
5x+5⋅-5+3(x+5)(x+5)(x-5)
Multiply 5 by -5.
5x-25+3(x+5)(x+5)(x-5)
Apply the distributive property.
5x-25+3x+3⋅5(x+5)(x-5)
Multiply 3 by 5.
5x-25+3x+15(x+5)(x-5)
8x-25+15(x+5)(x-5)
8x-10(x+5)(x-5)
Factor 2 out of 8x-10.
Factor 2 out of 8x.
2(4x)-10(x+5)(x-5)
Factor 2 out of -10.
2(4x)+2(-5)(x+5)(x-5)
Factor 2 out of 2(4x)+2(-5).
2(4x-5)(x+5)(x-5)
2(4x-5)(x+5)(x-5)
2(4x-5)(x+5)(x-5)
Simplify 5/(x+5)+3/(x-5)