Add 3/(x-6)+4/(x+5)

Math
3x-6+4x+5
To write 3x-6 as a fraction with a common denominator, multiply by x+5x+5.
3x-6⋅x+5x+5+4x+5
To write 4x+5 as a fraction with a common denominator, multiply by x-6x-6.
3x-6⋅x+5x+5+4x+5⋅x-6x-6
Write each expression with a common denominator of (x-6)(x+5), by multiplying each by an appropriate factor of 1.
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Multiply 3x-6 and x+5x+5.
3(x+5)(x-6)(x+5)+4x+5⋅x-6x-6
Multiply 4x+5 and x-6x-6.
3(x+5)(x-6)(x+5)+4(x-6)(x+5)(x-6)
Reorder the factors of (x-6)(x+5).
3(x+5)(x+5)(x-6)+4(x-6)(x+5)(x-6)
3(x+5)(x+5)(x-6)+4(x-6)(x+5)(x-6)
Combine the numerators over the common denominator.
3(x+5)+4(x-6)(x+5)(x-6)
Simplify the numerator.
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Apply the distributive property.
3x+3⋅5+4(x-6)(x+5)(x-6)
Multiply 3 by 5.
3x+15+4(x-6)(x+5)(x-6)
Apply the distributive property.
3x+15+4x+4⋅-6(x+5)(x-6)
Multiply 4 by -6.
3x+15+4x-24(x+5)(x-6)
Add 3x and 4x.
7x+15-24(x+5)(x-6)
Subtract 24 from 15.
7x-9(x+5)(x-6)
7x-9(x+5)(x-6)
Add 3/(x-6)+4/(x+5)

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