Question 976336
Guessing you mean, {{{d=LR^2/(R^2+R^1)}}}.


{{{d(R^2+R)=LR^2}}}

{{{dR^2+dR=LR^2}}}
{{{dR^2-LR^2+dR=0}}}
{{{(d-L)R^2+dR=0}}}
{{{R((d-L)R+d)=0}}}


{{{(d-L)R+d=0}}}
{{{(d-L)R=-d}}}
{{{R=-d/(d-L)}}}
{{{highlight(R=d/(L-d))}}}


The other zero-product choice of R=0 must be rejected because the original equation is undefined for R=0.



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The equation as posted was wrong.


SUBSCRIPTS Instead of exponents:
{{{d=(LR[2])/(R[2]+R[1])}}}


Multiplicative Inverse Property:
{{{d(R[2]+R[1])=LR[2]}}}


Distributive Property:
{{{dR[2]+dR[1]=LR[2]}}}


Additive Inverse of {{{dR[2]}}},
{{{dR[1]=LR[2]-dR[2]}}}


Multiplicative Property of Equality using multiplicative inverse of d,
{{{(1/d)dR[1]=(1/d)(LR[2]-dR[2])}}}


Simplification or other convenient adjustment,
{{{highlight(R[1]=(LR[2]-dR[2])/d)}}}