SOLUTION: How do I solve for t given the rational eqution: 1/t+5/(t+1)=10

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do I solve for t given the rational eqution: 1/t+5/(t+1)=10      Log On


   

Question 461745: How do I solve for t given the rational eqution: 1/t+5/(t+1)=10
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1%2Ft%2B5%2F%28t%2B1%29=10
%281%28t%2B1%29%2B5t%29%2Ft%28t%2B1%29=10
%281%28t%2B1%29%2B5t%29=10%2At%28t%2B1%29
t%2B1%2B5t=10%28t%5E2%2Bt%29
6t%2B1=10t%5E2%2B10t%29
0=10t%5E2%2B10t-6t-1%29

t+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A10%2A%28-1%29+%29%29%2F%282%2A10%29+

t+=+%28-4+%2B-+sqrt%28+16%2B40+%29%29%2F20+
t+=+%28-4+%2B-+sqrt%28+56+%29%29%2F20+
t+=+%28-4+%2B-+7.48%29%2F20+
solutions:
t+=+%28-4+%2B+7.48%29%2F20+
t+=+3.48%2F20+
t+=+0.174+
or
t+=+%28-4+-+7.48%29%2F20+
t+=+-11.48%2F20+
t+=+-0.574+

check the results:
1%2Ft%2B5%2F%28t%2B1%29=10
1%2F0.174%2B5%2F%280.174%2B1%29=10
5.75%2B5%2F%281.174%29=10
5.75%2B4.26=10
5.75%2B4.26=10
10.01=10
10=10