SOLUTION: These do not come from a textbook; only a worksheet. Please help! Thanks. 1. Solve the equation. t/t-2 = 7/t-2 + 2 2. Solve for x. x + 5 + x/x-5 = 5/x-5

Algebra ->  Equations -> SOLUTION: These do not come from a textbook; only a worksheet. Please help! Thanks. 1. Solve the equation. t/t-2 = 7/t-2 + 2 2. Solve for x. x + 5 + x/x-5 = 5/x-5      Log On


   

Question 95623: These do not come from a textbook; only a worksheet. Please help! Thanks.
1. Solve the equation.
t/t-2 = 7/t-2 + 2
2. Solve for x.
x + 5 + x/x-5 = 5/x-5
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1. Solve the equation.
t%2F%28t-2%29 = 7%2F%28t-2%29 + 2
:
WE can get rid of the denominators by multiplying equation by(t-2) like this:
(t-2)t%2F%28t-2%29 = (t-2)7%2F%28t-2%29 + 2(t-2)
:
Cancel out the denominators leaving you with:
t = 7 + 2(t-2)
t = 7 + 2t - 4: multiplied what's inside the brackets
t = 2t + 3
t - 2t = 3; subtracted 2t from both sides
-t = 3
t = -3; multiplied equation by -1, we always want the variable to be positive
:
Check solution in original equation:
%28-3%29%2F%28-3-2%29 = 7%2F%28-3-2%29 + 2
:
%28-3%29%2F%28-5%29 = 7%2F%28-5%29 + 10%2F5
which is:
+3%2F5 = -7%2F5 + 10%2F5
:
:
2. Solve for x.
x + 5 + x%2F%28x-5%29 = 5%2F%28x-5%29
Multiply equation by (x-5) to get rid of the denominators
x(x-5) + 5(x-5) + (x-5)x%2F%28x-5%29 = (x-5)5%2F%28x-5%29
:
x^2 - 5x + 5x - 25 + x = 5
x^2 + x - 25 - 5 = 0
x^2 + x - 30 = 0; a quadratic equation:
Factors to:
(x+6)(x-5) = 0
x = -6
and
x = +5
:
Check solution using x = -6 in original equation:
-6 + 5 + %28-6%29%2F%28-6-5%29 = 5%2F%28-6-5%29
:
-1 + %28-6%29%2F%28-11%29 = 5%2F%28-11%29
:
-11%2F11 + %286%29%2F%2811%29 = -5%2F%2811%29
:
I better point out to you that x=+5 is not a solution, it puts a 0 as the
denominator in the original equation, a big no-no in algebra