Question

How do I combine this expression?
\[
(6-t)^\frac{2}{3}-\frac{2t}{3}(6-t)^\frac{-1}{3}
\]

Answer 1

Question edited. Please refresh.

Answer 2

\[(6-t)^{\frac{2}{3}}-\frac{2t}{3(x-t)^{\frac{1}{3}}}\]
now add like with fractions

Answer 3

I think
=1/(6-t)^(1/3)[6-t-2t/3]
=1/(6-t)^(1/3)[(18-5t)/3]

Answer 4

\[\frac{(6-t)^{\frac{2}{3}}\times3(6-t)^{\frac{1}{3}}-2t}{3(6-t)^{\frac{1}{3}}}\]

Answer 5

Then I am stuck at your step. My brain isn't functioning properly today... @satellite73

Answer 6

\[\frac{(6-t)-2t}{3(6-t)^{\frac{1}{3}}}=\frac{6-3t}{3(6-t)^{\frac{1}{3}}}=\frac{2-t}{(6-t)^{\frac{1}{3}}}\]

Answer 7

which step, one or two?

Answer 8

Step two, but isn't the third post incorrect. I think it should look like this.
\[
\begin{align*}
&\frac{(6-t)^{\frac{2}{3}}\times3(6-t)^{\frac{1}{3}}-2t}{3(6-t)^{\frac{1}{3}}} \\
=&\frac{3(6-t)-2t}{3(6-t)^\frac{1}{3}} \\
=&\frac{18-5t}{3(6-t)^\frac{1}{3}}
\end{align*}
\]

Answer 9

yeah you got me. i forgot about that 3 in the numerator didn't i?

Answer 10

step 2 is because
\[a-\frac{b}{c}=\frac{ac-b}{c}\]