Question 122822
 
{{{(2y+3)/(4y-1)=(3y-1)/(3y+2)}}}.........first cross multiply 


{{{(2y+3)(3y+2)=(3y-1)(4y-1)}}}.........

	
{{{6y^2 + 4y + 9y + 6 = 12y^2 – 3y – 8y + 2}}}……

{{{6y^2 + 13y + 6 = 12y^2 – 11y + 2}}}……

{{{0 = 12y^2 - 6y^2 - 13y – 11y -6 + 2}}}……

{{{ 6y^2 - 24y – 4 = 0}}}……


{{{ y[1,2]    = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{ y[1,2]   = (-(-24) +- sqrt( (-24)^2 - 4*6*(-4) ))/(2*6) }}}

{{{ y[1,2]    = (24 +- sqrt(576 + 96))/12 }}}

{{{ y[1,2]   = (24 +- sqrt(672))/12 }}}	


{{{ y[1]   = (24 +- 25.92)/12 }}}

{{{ y[1]   = (24 + 25.92)/12 }}}

{{{ y[1]  =  4.16 }}}


{{{ y[2]  = (24 - 25.92)/12 }}}

{{{ y[2]  = ( - 1.92)/12 }}}

{{{y[2] = -0.16 }}}

Check:

If {{{ y[1]  =  4.16 }}}

{{{(2(4.16 )+3)/(4(4.16 )-1)=(3(4.16 )-1)/(3(4.16 )+2)}}}.........


{{{(8.32 +3)/(16.64 -1)=(12.48 -1)/(12.48 +2)}}}.........


{{{11.32 /15.64 = 10.48 /14.48 }}}……

{{{11.32 /15.64 = 10.48 /14.48 }}}……

{{{0.7237=0.7237}}}