Divide ((12x^2-14x+4)/(3x))÷((3x^2+x-2)/(2x^2+2x))

Math
12×2-14x+43x÷3×2+x-22×2+2x
To divide by a fraction, multiply by its reciprocal.
12×2-14x+43x⋅2×2+2x3x2+x-2
Simplify the numerator.
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Factor 2 out of 12×2-14x+4.
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Factor 2 out of 12×2.
2(6×2)-14x+43x⋅2×2+2x3x2+x-2
Factor 2 out of -14x.
2(6×2)+2(-7x)+43x⋅2×2+2x3x2+x-2
Factor 2 out of 4.
2(6×2)+2(-7x)+2(2)3x⋅2×2+2x3x2+x-2
Factor 2 out of 2(6×2)+2(-7x).
2(6×2-7x)+2(2)3x⋅2×2+2x3x2+x-2
Factor 2 out of 2(6×2-7x)+2(2).
2(6×2-7x+2)3x⋅2×2+2x3x2+x-2
2(6×2-7x+2)3x⋅2×2+2x3x2+x-2
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=6⋅2=12 and whose sum is b=-7.
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Factor -7 out of -7x.
2(6×2-7(x)+2)3x⋅2×2+2x3x2+x-2
Rewrite -7 as -3 plus -4
2(6×2+(-3-4)x+2)3x⋅2×2+2x3x2+x-2
Apply the distributive property.
2(6×2-3x-4x+2)3x⋅2×2+2x3x2+x-2
2(6×2-3x-4x+2)3x⋅2×2+2x3x2+x-2
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
2((6×2-3x)-4x+2)3x⋅2×2+2x3x2+x-2
Factor out the greatest common factor (GCF) from each group.
2(3x(2x-1)-2(2x-1))3x⋅2×2+2x3x2+x-2
2(3x(2x-1)-2(2x-1))3x⋅2×2+2x3x2+x-2
Factor the polynomial by factoring out the greatest common factor, 2x-1.
2((2x-1)(3x-2))3x⋅2×2+2x3x2+x-2
2(2x-1)(3x-2)3x⋅2×2+2x3x2+x-2
2(2x-1)(3x-2)3x⋅2×2+2x3x2+x-2
Factor 2x out of 2×2+2x.
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Factor 2x out of 2×2.
2(2x-1)(3x-2)3x⋅2x(x)+2x3x2+x-2
Factor 2x out of 2x.
2(2x-1)(3x-2)3x⋅2x(x)+2x(1)3×2+x-2
Factor 2x out of 2x(x)+2x(1).
2(2x-1)(3x-2)3x⋅2x(x+1)3×2+x-2
2(2x-1)(3x-2)3x⋅2x(x+1)3×2+x-2
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=3⋅-2=-6 and whose sum is b=1.
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Multiply by 1.
2(2x-1)(3x-2)3x⋅2x(x+1)3×2+1x-2
Rewrite 1 as -2 plus 3
2(2x-1)(3x-2)3x⋅2x(x+1)3×2+(-2+3)x-2
Apply the distributive property.
2(2x-1)(3x-2)3x⋅2x(x+1)3×2-2x+3x-2
2(2x-1)(3x-2)3x⋅2x(x+1)3×2-2x+3x-2
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
2(2x-1)(3x-2)3x⋅2x(x+1)(3×2-2x)+3x-2
Factor out the greatest common factor (GCF) from each group.
2(2x-1)(3x-2)3x⋅2x(x+1)x(3x-2)+1(3x-2)
2(2x-1)(3x-2)3x⋅2x(x+1)x(3x-2)+1(3x-2)
Factor the polynomial by factoring out the greatest common factor, 3x-2.
2(2x-1)(3x-2)3x⋅2x(x+1)(3x-2)(x+1)
2(2x-1)(3x-2)3x⋅2x(x+1)(3x-2)(x+1)
Cancel the common factor of 3x-2.
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Factor 3x-2 out of 2(2x-1)(3x-2).
(3x-2)(2(2x-1))3x⋅2x(x+1)(3x-2)(x+1)
Cancel the common factor.
(3x-2)(2(2x-1))3x⋅2x(x+1)(3x-2)(x+1)
Rewrite the expression.
2(2x-1)3x⋅2x(x+1)x+1
2(2x-1)3x⋅2x(x+1)x+1
Cancel the common factor of x.
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Factor x out of 3x.
2(2x-1)x⋅3⋅2x(x+1)x+1
Factor x out of 2x(x+1).
2(2x-1)x⋅3⋅x(2(x+1))x+1
Cancel the common factor.
2(2x-1)x⋅3⋅x(2(x+1))x+1
Rewrite the expression.
2(2x-1)3⋅2(x+1)x+1
2(2x-1)3⋅2(x+1)x+1
Multiply 2(2x-1)3 and 2(x+1)x+1.
2(2x-1)(2(x+1))3(x+1)
Multiply 2 by 2.
4(2x-1)(x+1)3(x+1)
Cancel the common factor of x+1.
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Cancel the common factor.
4(2x-1)(x+1)3(x+1)
Rewrite the expression.
4(2x-1)3
4(2x-1)3
Apply the distributive property.
4(2x)+4⋅-13
Multiply 2 by 4.
8x+4⋅-13
Multiply 4 by -1.
8x-43
Split the fraction 8x-43 into two fractions.
8×3+-43
Move the negative in front of the fraction.
8×3-43
Divide ((12x^2-14x+4)/(3x))÷((3x^2+x-2)/(2x^2+2x))

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