Question

Solve for t. If there are multiple solutions, enter them as a

Answer 1

we have the equation

`(12)/(t)+(18)/((t-2))=(9)/(2)`

Solve for t

step 1

Multiply both sides by 2t(t-2) to remove fractions

`(12\cdot2t(t-2))/(t)+(18\cdot2t(t-2))/((t-2))=(9\cdot2t(t-2))/(2)`

simplify

`12\cdot2(t-2)+18\cdot2t=9\cdot t(t-2)`
`24t-48+36t=9t^2-18t`
`\begin{gathered} 60t-48=9t^2-18t \\ 9t^2-18t-60t+48=0 \\ 9t^2-78t+48=0 \end{gathered}`

Solve the quadratic equation

Using the formula

a=9

b=-78

c=48

substitute

`t=\frac{-(-78)\pm\sqrt[]{-78^2-4(9)(48)}}{2(9)}`
`t=(78\pm66)/(18)`

The solutions for t are

t=8 and t=2/3

therefore

the answer is

t=2/3,8