Question

1/b + 1/9 + = 1/tSolve for t

Answer 1

The given expression is

`(1)/(b)+(1)/(9)=(1)/(t)`

First, we multiply the equation by t

`\begin{gathered} ((1)/(b)+(1)/(9))\cdot t=(1)/(t)\cdot t \\ ((1)/(b)+(1)/(9))\cdot t=1 \end{gathered}`

Now, we divide the equation by 1/b + 1/9

`\begin{gathered} (((1)/(b)+(1)/(9))\cdot t)/(((1)/(b)+(1)/(9)))=(1)/(((1)/(b)+(1)/(9))) \\ t=(1)/(((1)/(b)+(1)/(9))) \end{gathered}`

Now, we sum fractions

`t=(1)/((9+b)/(9b))`

Then, we solve this combined fraction

`t=(9b\cdot1)/(9+b)=(9b)/(9+b)`

Therefore, the final expression is

`t=(9b)/(9+b)`