# Simplify (5x-3)/(7x+3)+(8x^2+3)/(7x+1)

5x-37x+3+8×2+37x+1
To write 5x-37x+3 as a fraction with a common denominator, multiply by 7x+17x+1.
5x-37x+3⋅7x+17x+1+8×2+37x+1
To write 8×2+37x+1 as a fraction with a common denominator, multiply by 7x+37x+3.
5x-37x+3⋅7x+17x+1+8×2+37x+1⋅7x+37x+3
Write each expression with a common denominator of (7x+3)(7x+1), by multiplying each by an appropriate factor of 1.
Multiply 5x-37x+3 and 7x+17x+1.
(5x-3)(7x+1)(7x+3)(7x+1)+8×2+37x+1⋅7x+37x+3
Multiply 8×2+37x+1 and 7x+37x+3.
(5x-3)(7x+1)(7x+3)(7x+1)+(8×2+3)(7x+3)(7x+1)(7x+3)
Reorder the factors of (7x+3)(7x+1).
(5x-3)(7x+1)(7x+1)(7x+3)+(8×2+3)(7x+3)(7x+1)(7x+3)
(5x-3)(7x+1)(7x+1)(7x+3)+(8×2+3)(7x+3)(7x+1)(7x+3)
Combine the numerators over the common denominator.
(5x-3)(7x+1)+(8×2+3)(7x+3)(7x+1)(7x+3)
Simplify the numerator.
Expand (5x-3)(7x+1) using the FOIL Method.
Apply the distributive property.
5x(7x+1)-3(7x+1)+(8×2+3)(7x+3)(7x+1)(7x+3)
Apply the distributive property.
5x(7x)+5x⋅1-3(7x+1)+(8×2+3)(7x+3)(7x+1)(7x+3)
Apply the distributive property.
5x(7x)+5x⋅1-3(7x)-3⋅1+(8×2+3)(7x+3)(7x+1)(7x+3)
5x(7x)+5x⋅1-3(7x)-3⋅1+(8×2+3)(7x+3)(7x+1)(7x+3)
Simplify and combine like terms.
Simplify each term.
Multiply x by x.
5⋅7×2+5x⋅1-3(7x)-3⋅1+(8×2+3)(7x+3)(7x+1)(7x+3)
Multiply 5 by 7.
35×2+5x⋅1-3(7x)-3⋅1+(8×2+3)(7x+3)(7x+1)(7x+3)
Multiply 5 by 1.
35×2+5x-3(7x)-3⋅1+(8×2+3)(7x+3)(7x+1)(7x+3)
Multiply 7 by -3.
35×2+5x-21x-3⋅1+(8×2+3)(7x+3)(7x+1)(7x+3)
Multiply -3 by 1.
35×2+5x-21x-3+(8×2+3)(7x+3)(7x+1)(7x+3)
35×2+5x-21x-3+(8×2+3)(7x+3)(7x+1)(7x+3)
Subtract 21x from 5x.
35×2-16x-3+(8×2+3)(7x+3)(7x+1)(7x+3)
35×2-16x-3+(8×2+3)(7x+3)(7x+1)(7x+3)
Expand (8×2+3)(7x+3) using the FOIL Method.
Apply the distributive property.
35×2-16x-3+8×2(7x+3)+3(7x+3)(7x+1)(7x+3)
Apply the distributive property.
35×2-16x-3+8×2(7x)+8×2⋅3+3(7x+3)(7x+1)(7x+3)
Apply the distributive property.
35×2-16x-3+8×2(7x)+8×2⋅3+3(7x)+3⋅3(7x+1)(7x+3)
35×2-16x-3+8×2(7x)+8×2⋅3+3(7x)+3⋅3(7x+1)(7x+3)
Simplify each term.
Rewrite using the commutative property of multiplication.
35×2-16x-3+8⋅7(x2x)+8×2⋅3+3(7x)+3⋅3(7x+1)(7x+3)
Multiply x2 by x by adding the exponents.
Multiply x2 by x.
Raise x to the power of 1.
35×2-16x-3+8⋅7(x2x1)+8×2⋅3+3(7x)+3⋅3(7x+1)(7x+3)
Use the power rule aman=am+n to combine exponents.
35×2-16x-3+8⋅7×2+1+8×2⋅3+3(7x)+3⋅3(7x+1)(7x+3)
35×2-16x-3+8⋅7×2+1+8×2⋅3+3(7x)+3⋅3(7x+1)(7x+3)
35×2-16x-3+8⋅7×3+8×2⋅3+3(7x)+3⋅3(7x+1)(7x+3)
35×2-16x-3+8⋅7×3+8×2⋅3+3(7x)+3⋅3(7x+1)(7x+3)
Multiply 8 by 7.
35×2-16x-3+56×3+8×2⋅3+3(7x)+3⋅3(7x+1)(7x+3)
Multiply 3 by 8.
35×2-16x-3+56×3+24×2+3(7x)+3⋅3(7x+1)(7x+3)
Multiply 7 by 3.
35×2-16x-3+56×3+24×2+21x+3⋅3(7x+1)(7x+3)
Multiply 3 by 3.
35×2-16x-3+56×3+24×2+21x+9(7x+1)(7x+3)
35×2-16x-3+56×3+24×2+21x+9(7x+1)(7x+3)
59×2-16x-3+56×3+21x+9(7x+1)(7x+3)
59×2+5x-3+56×3+9(7x+1)(7x+3)
59×2+5x+56×3+6(7x+1)(7x+3)
Reorder terms.
56×3+59×2+5x+6(7x+1)(7x+3)
56×3+59×2+5x+6(7x+1)(7x+3)
Simplify (5x-3)/(7x+3)+(8x^2+3)/(7x+1)

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