# Simplify (1/7+4/y)/(1/9-8/y)

17+4y19-8y
Multiply the numerator and denominator of the complex fraction by 63y.
Multiply 17+4y19-8y by 63y63y.
63y63y⋅17+4y19-8y
Combine.
63y(17+4y)63y(19-8y)
63y(17+4y)63y(19-8y)
Apply the distributive property.
63y17+63y4y63y19+63y(-8y)
Simplify by cancelling.
Cancel the common factor of 7.
Factor 7 out of 63y.
7(9y)17+63y4y63y19+63y(-8y)
Cancel the common factor.
7(9y)17+63y4y63y19+63y(-8y)
Rewrite the expression.
9y+63y4y63y19+63y(-8y)
9y+63y4y63y19+63y(-8y)
Cancel the common factor of y.
Factor y out of 63y.
9y+y⋅634y63y19+63y(-8y)
Cancel the common factor.
9y+y⋅634y63y19+63y(-8y)
Rewrite the expression.
9y+63⋅463y19+63y(-8y)
9y+63⋅463y19+63y(-8y)
Multiply 63 by 4.
9y+25263y19+63y(-8y)
Cancel the common factor of 9.
Factor 9 out of 63y.
9y+2529(7y)19+63y(-8y)
Cancel the common factor.
9y+2529(7y)19+63y(-8y)
Rewrite the expression.
9y+2527y+63y(-8y)
9y+2527y+63y(-8y)
Cancel the common factor of y.
Move the leading negative in -8y into the numerator.
9y+2527y+63y-8y
Factor y out of 63y.
9y+2527y+y⋅63-8y
Cancel the common factor.
9y+2527y+y⋅63-8y
Rewrite the expression.
9y+2527y+63⋅-8
9y+2527y+63⋅-8
Multiply 63 by -8.
9y+2527y-504
9y+2527y-504
Simplify with factoring out.
Factor 9 out of 9y+252.
Factor 9 out of 9y.
9(y)+2527y-504
Factor 9 out of 252.
9y+9⋅287y-504
Factor 9 out of 9y+9⋅28.
9(y+28)7y-504
9(y+28)7y-504
Factor 7 out of 7y-504.
Factor 7 out of 7y.
9(y+28)7(y)-504
Factor 7 out of -504.
9(y+28)7y+7⋅-72
Factor 7 out of 7y+7⋅-72.
9(y+28)7(y-72)
9(y+28)7(y-72)
9(y+28)7(y-72)
Simplify (1/7+4/y)/(1/9-8/y)

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