Add (2x+3)/(x-4)+3/(x+8)

Math
2x+3x-4+3x+8
To write 2x+3x-4 as a fraction with a common denominator, multiply by x+8x+8.
2x+3x-4⋅x+8x+8+3x+8
To write 3x+8 as a fraction with a common denominator, multiply by x-4x-4.
2x+3x-4⋅x+8x+8+3x+8⋅x-4x-4
Write each expression with a common denominator of (x-4)(x+8), by multiplying each by an appropriate factor of 1.
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Multiply 2x+3x-4 and x+8x+8.
(2x+3)(x+8)(x-4)(x+8)+3x+8⋅x-4x-4
Multiply 3x+8 and x-4x-4.
(2x+3)(x+8)(x-4)(x+8)+3(x-4)(x+8)(x-4)
Reorder the factors of (x-4)(x+8).
(2x+3)(x+8)(x+8)(x-4)+3(x-4)(x+8)(x-4)
(2x+3)(x+8)(x+8)(x-4)+3(x-4)(x+8)(x-4)
Combine the numerators over the common denominator.
(2x+3)(x+8)+3(x-4)(x+8)(x-4)
Simplify the numerator.
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Expand (2x+3)(x+8) using the FOIL Method.
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Apply the distributive property.
2x(x+8)+3(x+8)+3(x-4)(x+8)(x-4)
Apply the distributive property.
2x⋅x+2x⋅8+3(x+8)+3(x-4)(x+8)(x-4)
Apply the distributive property.
2x⋅x+2x⋅8+3x+3⋅8+3(x-4)(x+8)(x-4)
2x⋅x+2x⋅8+3x+3⋅8+3(x-4)(x+8)(x-4)
Simplify and combine like terms.
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Simplify each term.
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Multiply x by x by adding the exponents.
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Move x.
2(x⋅x)+2x⋅8+3x+3⋅8+3(x-4)(x+8)(x-4)
Multiply x by x.
2×2+2x⋅8+3x+3⋅8+3(x-4)(x+8)(x-4)
2×2+2x⋅8+3x+3⋅8+3(x-4)(x+8)(x-4)
Multiply 8 by 2.
2×2+16x+3x+3⋅8+3(x-4)(x+8)(x-4)
Multiply 3 by 8.
2×2+16x+3x+24+3(x-4)(x+8)(x-4)
2×2+16x+3x+24+3(x-4)(x+8)(x-4)
Add 16x and 3x.
2×2+19x+24+3(x-4)(x+8)(x-4)
2×2+19x+24+3(x-4)(x+8)(x-4)
Apply the distributive property.
2×2+19x+24+3x+3⋅-4(x+8)(x-4)
Multiply 3 by -4.
2×2+19x+24+3x-12(x+8)(x-4)
Add 19x and 3x.
2×2+22x+24-12(x+8)(x-4)
Subtract 12 from 24.
2×2+22x+12(x+8)(x-4)
Factor 2 out of 2×2+22x+12.
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Factor 2 out of 2×2.
2(x2)+22x+12(x+8)(x-4)
Factor 2 out of 22x.
2(x2)+2(11x)+12(x+8)(x-4)
Factor 2 out of 12.
2×2+2(11x)+2⋅6(x+8)(x-4)
Factor 2 out of 2×2+2(11x).
2(x2+11x)+2⋅6(x+8)(x-4)
Factor 2 out of 2(x2+11x)+2⋅6.
2(x2+11x+6)(x+8)(x-4)
2(x2+11x+6)(x+8)(x-4)
2(x2+11x+6)(x+8)(x-4)
Add (2x+3)/(x-4)+3/(x+8)

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