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

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) (Show Source): You can put this solution on YOUR website!
1. Solve the equation.
= + 2
:
WE can get rid of the denominators by multiplying equation by(t-2) like this:
(t-2) = (t-2) + 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:
= + 2
:
= +
which is:
+ = +
:
:
2. Solve for x.
x + 5 + =
Multiply equation by (x-5) to get rid of the denominators
x(x-5) + 5(x-5) + (x-5) = (x-5)
:
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 + =
:
-1 + =
:
+ =
:
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

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