Question 340958
First simplify.
{{{(8x^2 y/z^3)^2=(64x^4y^2)/(z^6)}}}
Dividing by a fraction is equivalent to multiplying by its reciprocal.
{{{((4xy^3)/(z^2))/((8x^2 y)/(z^3))^2=((4xy^3)/(z^2))*(z^6/(64x^4y^2))}}}
{{{((4xy^3)/(z^2))/((8x^2 y)/(z^3))^2=(4/64)x^(1-4)y^(3-2)z^(6-2)}}}
{{{((4xy^3)/(z^2))/((8x^2 y)/(z^3))^2=(1/16)x^(-3)y^(1)z^(4)}}}
{{{((4xy^3)/(z^2))/((8x^2 y)/(z^3))^2=highlight((yz^(4))/(16x^3))}}}

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Use the common denominator,{{{d^2 - 9=(d-3)(d+3)}}}
{{{5/(2d + 6)=(5/2)/(d+3)}}}
{{{5/(2d + 6)=((5/2)(d-3))/((d-3)(d+3))}}}
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 {{{(d)/(d^2 - 9) + 5/(2d + 6)=(d)/((d-3)(d+3))+((5/2)(d-3))/((d-3)(d+3))}}}
{{{(d)/(d^2 - 9) + 5/(2d + 6)=(d+((5/2)(d-3)))/((d-3)(d+3))}}}
{{{(d)/(d^2 - 9) + 5/(2d + 6)=((2/2)d+(5/2)(d)-15/2)/((d-3)(d+3))}}}
{{{(d)/(d^2 - 9) + 5/(2d + 6)=((7/2)(d)-15/2)/((d-3)(d+3))}}}
{{{(d)/(d^2 - 9) + 5/(2d + 6)=highlight((7d-15)/(2(d-3)(d+3)))}}}