Simplify (y-(3y-7)/7)/(28/14+7/(2y))

Math
y-3y-772814+72y
Cancel the common factor of 28 and 14.
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Factor 14 out of 28.
y-3y-7714⋅214+72y
Cancel the common factors.
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Factor 14 out of 14.
y-3y-7714⋅214(1)+72y
Cancel the common factor.
y-3y-7714⋅214⋅1+72y
Rewrite the expression.
y-3y-7721+72y
Divide 2 by 1.
y-3y-772+72y
y-3y-772+72y
y-3y-772+72y
Multiply the numerator and denominator of the complex fraction by 14y.
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Multiply y-3y-772+72y by 14y14y.
14y14y⋅y-3y-772+72y
Combine.
14y(y-3y-77)14y(2+72y)
14y(y-3y-77)14y(2+72y)
Apply the distributive property.
14y⋅y+14y(-3y-77)14y⋅2+14y72y
Simplify by cancelling.
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Cancel the common factor of 7.
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Move the leading negative in -3y-77 into the numerator.
14y⋅y+14y-(3y-7)714y⋅2+14y72y
Factor 7 out of 14y.
14y⋅y+7(2y)-(3y-7)714y⋅2+14y72y
Cancel the common factor.
14y⋅y+7(2y)-(3y-7)714y⋅2+14y72y
Rewrite the expression.
14y⋅y+2y(-(3y-7))14y⋅2+14y72y
14y⋅y+2y(-(3y-7))14y⋅2+14y72y
Multiply -1 by 2.
14y⋅y-2y(3y-7)14y⋅2+14y72y
Cancel the common factor of 2y.
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Factor 2y out of 14y.
14y⋅y-2y(3y-7)14y⋅2+2y(7)72y
Cancel the common factor.
14y⋅y-2y(3y-7)14y⋅2+2y⋅772y
Rewrite the expression.
14y⋅y-2y(3y-7)14y⋅2+7⋅7
14y⋅y-2y(3y-7)14y⋅2+7⋅7
Multiply 7 by 7.
14y⋅y-2y(3y-7)14y⋅2+49
14y⋅y-2y(3y-7)14y⋅2+49
Simplify the numerator.
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Multiply y by y by adding the exponents.
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Move y.
14(y⋅y)-2y(3y-7)14y⋅2+49
Multiply y by y.
14y2-2y(3y-7)14y⋅2+49
14y2-2y(3y-7)14y⋅2+49
Apply the distributive property.
14y2-2y(3y)-2y⋅-714y⋅2+49
Multiply y by y.
14y2-2⋅3y2-2y⋅-714y⋅2+49
Multiply -7 by -2.
14y2-2⋅3y2+14y14y⋅2+49
Multiply -2 by 3.
14y2-6y2+14y14y⋅2+49
Subtract 6y2 from 14y2.
8y2+14y14y⋅2+49
Factor 2y out of 8y2+14y.
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Factor 2y out of 8y2.
2y(4y)+14y14y⋅2+49
Factor 2y out of 14y.
2y(4y)+2y(7)14y⋅2+49
Factor 2y out of 2y(4y)+2y(7).
2y(4y+7)14y⋅2+49
2y(4y+7)14y⋅2+49
2y(4y+7)14y⋅2+49
Simplify the denominator.
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Factor 7 out of 14y⋅2+49.
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Factor 7 out of 14y⋅2.
2y(4y+7)7(2y⋅2)+49
Factor 7 out of 49.
2y(4y+7)7(2y⋅2)+7(7)
Factor 7 out of 7(2y⋅2)+7(7).
2y(4y+7)7(2y⋅2+7)
2y(4y+7)7(2y⋅2+7)
Multiply 2 by 2.
2y(4y+7)7(4y+7)
2y(4y+7)7(4y+7)
Cancel the common factor of 4y+7.
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Cancel the common factor.
2y(4y+7)7(4y+7)
Rewrite the expression.
2y7
2y7
Simplify (y-(3y-7)/7)/(28/14+7/(2y))

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