Help with an algebra question?

Question

Express in simplest form:

1/2t+2 + 1/t - 1/t^2+t

I got 3/2t+1 but I'm pretty sure it's wrong. Can somebody show me how to get the right answer?

Answer 1

I will assume that you mean

1/(2t+2) + 1/t - 1/(t^2+t)

1)  Factor the numerators (nothing to do here).

2)  Factor the denominators:

        2t+2 = 2(t+1)

        t^2+t = t(t+1)

3)  Cancel factors in numerators with factors in denominators

        (nothing to do here)

4)  Find the least common denominator (LCD) by including all the

        factors in all three denominators.

     The first two denominators give us 2(t+1)t.

     Nothing new in the third denominator.  LCD = 2(t+1)t,

5)  Write all three terms with the LCD and add/subtract.

         1/2(t+1) =      ............   t/2(t+1)t

      + 1/t =   ....... +  2(t+1)/2(t+1)t

      -  1/t(t+1) =  ..........-  2/2(t+1)t

for: t + 2(t+1) - 2 = 3t / 2(t+1)t  = 3 / 2(t+1).

Either I misread your equation or you came pretty close.

Answer 2

1 /(2t+2) + 1 /t - 1 /(t^2-t)

First, find the common denominator for (2t+2), t, (t^2+t)

2t+2 = 2(t+1)

t^2+t = t(t+1)

t is already in t(t+1)

so the common denominator is 2t(t+1)

Now change each fraction to the common denominator

1/(2t+2) * t/t = t/2t(t+1)

1/t * 2(t+1)/2(t+1) = 2(t+1) /2t(t+1)

1/(t^2+t) *2/2 = 2/2t(t+1)

Now combine the numerators.

t + 2(t+1) - 2 = 3t

The answer is 3t/2t(t+1)

factor out the t top and bottom

3/2(t+1) or 3/(2t+2)

you only missed the parentheses