Work Step by Step
In order to solve rational equations, we try to get the variable by itself on one side of the equation. It is important to remember that there are many ways to do this. For instance, we could combine the different fractions and then simplify, or we could multiply both sides of the equation by the least common denominator. In addition, we may need previously learned methods of solving equations, such as factoring. Thus, solving the rational equation, we obtain: $$ \left(t-12\right)\left(10-t\right)=\left(t-10\right)\cdot \:1\\ t=10,\:t=11$$ Since $t=10$ makes a denominator zero, this is not a valid solution.