seems we undistributed the [tex]( \frac{5}{2} )^x[/tex]
remember [tex]x^{a+b}=(x^a)(x^b)[/tex] factor out [tex]( \frac{5}{2} )^x[/tex] from each term on the left side [tex]1( \frac{5}{2} )^x+( \frac{5}{2} )^3( \frac{5}{2} )^x=A( \frac{5}{2} )^x[/tex] undistribute [tex]( \frac{5}{2} )^x[/tex] [tex]( \frac{5}{2} )^x(1+( \frac{5}{2} )^3)=A( \frac{5}{2} )^x[/tex] divide both sides by [tex]( \frac{5}{2} )^x[/tex] [tex] 1+( \frac{5}{2} )^3=A [/tex]
