Question 461745


{{{1/t+5/(t+1)=10}}}

{{{(1(t+1)+5t)/t(t+1)=10}}}

{{{(1(t+1)+5t)=10*t(t+1)}}}

{{{t+1+5t=10(t^2+t)}}}

{{{6t+1=10t^2+10t)}}}

{{{0=10t^2+10t-6t-1)}}}

{{{10t^2+4t-1=0)}}...use quadratic formula

{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{t = (-4 +- sqrt( 4^2-4*10*(-1) ))/(2*10) }}}


{{{t = (-4 +- sqrt( 16+40 ))/20 }}}

{{{t = (-4 +- sqrt( 56 ))/20 }}}

{{{t = (-4 +- 7.48)/20 }}}

solutions:

{{{t = (-4 + 7.48)/20 }}}

{{{t = 3.48/20 }}}

{{{t = 0.174 }}}

or

{{{t = (-4 - 7.48)/20 }}}

{{{t = -11.48/20 }}}

{{{t = -0.574 }}}


check the results:

{{{1/t+5/(t+1)=10}}}

{{{1/0.174+5/(0.174+1)=10}}}

{{{5.75+5/(1.174)=10}}}

{{{5.75+4.26=10}}}

{{{5.75+4.26=10}}}

{{{10.01=10}}}

{{{10=10}}}