# Simplify (1/(y^2)+2/3)/(1/y-5/6)

1y2+231y-56
Multiply the numerator and denominator of the complex fraction by 6y2.
Multiply 1y2+231y-56 by 6y26y2.
6y26y2⋅1y2+231y-56
Combine.
6y2(1y2+23)6y2(1y-56)
6y2(1y2+23)6y2(1y-56)
Apply the distributive property.
6y21y2+6y2236y21y+6y2(-56)
Simplify by cancelling.
Cancel the common factor of y2.
Factor y2 out of 6y2.
y2⋅61y2+6y2236y21y+6y2(-56)
Cancel the common factor.
y2⋅61y2+6y2236y21y+6y2(-56)
Rewrite the expression.
6+6y2236y21y+6y2(-56)
6+6y2236y21y+6y2(-56)
Cancel the common factor of 3.
Factor 3 out of 6y2.
6+3(2y2)236y21y+6y2(-56)
Cancel the common factor.
6+3(2y2)236y21y+6y2(-56)
Rewrite the expression.
6+2y2⋅26y21y+6y2(-56)
6+2y2⋅26y21y+6y2(-56)
Multiply 2 by 2.
6+4y26y21y+6y2(-56)
Cancel the common factor of y.
Factor y out of 6y2.
6+4y2y(6y)1y+6y2(-56)
Cancel the common factor.
6+4y2y(6y)1y+6y2(-56)
Rewrite the expression.
6+4y26y+6y2(-56)
6+4y26y+6y2(-56)
Cancel the common factor of 6.
Move the leading negative in -56 into the numerator.
6+4y26y+6y2-56
Factor 6 out of 6y2.
6+4y26y+6(y2)-56
Cancel the common factor.
6+4y26y+6y2-56
Rewrite the expression.
6+4y26y+y2⋅-5
6+4y26y+y2⋅-5
6+4y26y+y2⋅-5
Factor 2 out of 6+4y2.
Factor 2 out of 6.
2(3)+4y26y+y2⋅-5
Factor 2 out of 4y2.
2(3)+2(2y2)6y+y2⋅-5
Factor 2 out of 2(3)+2(2y2).
2(3+2y2)6y+y2⋅-5
2(3+2y2)6y+y2⋅-5
Simplify the denominator.
Factor y out of 6y+y2⋅-5.
Factor y out of 6y.
2(3+2y2)y⋅6+y2⋅-5
Factor y out of y2⋅-5.
2(3+2y2)y⋅6+y(y⋅-5)
Factor y out of y⋅6+y(y⋅-5).
2(3+2y2)y(6+y⋅-5)
2(3+2y2)y(6+y⋅-5)
Move -5 to the left of y.
2(3+2y2)y(6-5y)
2(3+2y2)y(6-5y)
Simplify (1/(y^2)+2/3)/(1/y-5/6)

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