Divide ((x+3)/(4x+4))÷((x^2*(2x)-3)/(x^2-x-2))

Math
x+34x+4÷x2⋅(2x)-3×2-x-2
To divide by a fraction, multiply by its reciprocal.
x+34x+4⋅x2-x-2×2⋅(2x)-3
Factor 4 out of 4x+4.
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Factor 4 out of 4x.
x+34(x)+4⋅x2-x-2×2⋅(2x)-3
Factor 4 out of 4.
x+34(x)+4(1)⋅x2-x-2×2⋅(2x)-3
Factor 4 out of 4(x)+4(1).
x+34(x+1)⋅x2-x-2×2⋅(2x)-3
x+34(x+1)⋅x2-x-2×2⋅(2x)-3
Factor x2-x-2 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -2 and whose sum is -1.
-2,1
Write the factored form using these integers.
x+34(x+1)⋅(x-2)(x+1)x2⋅(2x)-3
x+34(x+1)⋅(x-2)(x+1)x2⋅(2x)-3
Simplify the denominator.
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Rewrite using the commutative property of multiplication.
x+34(x+1)⋅(x-2)(x+1)2x2x-3
Multiply x2 by x by adding the exponents.
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Move x.
x+34(x+1)⋅(x-2)(x+1)2(x⋅x2)-3
Multiply x by x2.
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Raise x to the power of 1.
x+34(x+1)⋅(x-2)(x+1)2(x1x2)-3
Use the power rule aman=am+n to combine exponents.
x+34(x+1)⋅(x-2)(x+1)2×1+2-3
x+34(x+1)⋅(x-2)(x+1)2×1+2-3
Add 1 and 2.
x+34(x+1)⋅(x-2)(x+1)2×3-3
x+34(x+1)⋅(x-2)(x+1)2×3-3
x+34(x+1)⋅(x-2)(x+1)2×3-3
Cancel the common factor of x+1.
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Factor x+1 out of 4(x+1).
x+3(x+1)⋅4⋅(x-2)(x+1)2×3-3
Factor x+1 out of (x-2)(x+1).
x+3(x+1)⋅4⋅(x+1)(x-2)2×3-3
Cancel the common factor.
x+3(x+1)⋅4⋅(x+1)(x-2)2×3-3
Rewrite the expression.
x+34⋅x-22×3-3
x+34⋅x-22×3-3
Multiply x+34 and x-22×3-3.
(x+3)(x-2)4(2×3-3)
Expand (x+3)(x-2) using the FOIL Method.
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Apply the distributive property.
x(x-2)+3(x-2)4(2×3-3)
Apply the distributive property.
x⋅x+x⋅-2+3(x-2)4(2×3-3)
Apply the distributive property.
x⋅x+x⋅-2+3x+3⋅-24(2×3-3)
x⋅x+x⋅-2+3x+3⋅-24(2×3-3)
Simplify and combine like terms.
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Simplify each term.
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Multiply x by x.
x2+x⋅-2+3x+3⋅-24(2×3-3)
Move -2 to the left of x.
x2-2⋅x+3x+3⋅-24(2×3-3)
Multiply 3 by -2.
x2-2x+3x-64(2×3-3)
x2-2x+3x-64(2×3-3)
Add -2x and 3x.
x2+x-64(2×3-3)
x2+x-64(2×3-3)
Split the fraction x2+x-64(2×3-3) into two fractions.
x2+x4(2×3-3)+-64(2×3-3)
Split the fraction x2+x4(2×3-3) into two fractions.
x24(2×3-3)+x4(2×3-3)+-64(2×3-3)
Cancel the common factor of -6 and 4.
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Factor 2 out of -6.
x24(2×3-3)+x4(2×3-3)+2(-3)4(2×3-3)
Cancel the common factors.
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Factor 2 out of 4(2×3-3).
x24(2×3-3)+x4(2×3-3)+2(-3)2(2(2×3-3))
Cancel the common factor.
x24(2×3-3)+x4(2×3-3)+2⋅-32(2(2×3-3))
Rewrite the expression.
x24(2×3-3)+x4(2×3-3)+-32(2×3-3)
x24(2×3-3)+x4(2×3-3)+-32(2×3-3)
x24(2×3-3)+x4(2×3-3)+-32(2×3-3)
Move the negative in front of the fraction.
x24(2×3-3)+x4(2×3-3)-32(2×3-3)
Divide ((x+3)/(4x+4))÷((x^2*(2x)-3)/(x^2-x-2))

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