Question 110329
make {{{x}}} the subject {{{y^2=(8x+2)^2/(4x+2)}}}

{{{y^2=(8x+2)(8x+2)/(4x+2)}}}

{{{y^2=2(4x+1)(8x+2)/2(2x+1)}}}....cancel {{{2}}} in both nominator and denominator


{{{y^2=(4x+1)(8x+2)/(2x+1)}}}......multiply terms in nominator


{{{y^2=(32x^2 + 8x + 8x + 2)/(2x+1)}}}......


{{{y^2=(32x^2 + 16x + 2)/(2x+1)}}}......divide each term in nominator by {{{2}}}


{{{y^2=(16x^2 + 8x + 1)/(2x+1)}}}......replace {{{8x}}} with {{{4x + 4x}}}


{{{y^2=(16x^2 + 4x+ 4x + 1)/(2x+1)}}}......group the first two terms together and the last two terms together


{{{y^2=((16x^2 + 4x)+ (4x + 1))/(2x+1)}}}......factor a {{{4x}}} out of the first group and {{{1}}} out of the second group

{{{y^2=(4x(4x + 1)+ 1(4x + 1))/(2x+1)}}}......we have a common term {{{(4x + 1)}}}

{{{y^2=(4x + 1)(4x + 1)/(2x+1)}}}......