Chapter 5.6, Problem 11WE

To determine

To simplify the given expression.

Answer to Problem 11WE

  $\frac{1}{6}$

Explanation of Solution

Given:

Expression: $\frac{t-4}{2t}-\frac{t-6}{3t}$

Calculation:

Consider the given expression $\frac{t-4}{2t}-\frac{t-6}{3t}$ ,

Since the denominators of both the fractions are different, find the least common denominator for both the fractions.

Here, least common denominator is $6t$ , so

  $\frac{t-4}{2t}-\frac{t-6}{3t}$

  $=\frac{\left(t-4\right)\cdot 3}{2t\cdot 3}-\frac{\left(t-6\right)\cdot 2}{3t\cdot 2}$

  $=\frac{3t-12}{6t}-\frac{2t-12}{6t}$

Now, as the denominators of the two fractions are same, simply subtract the numerators and put the result on the same denominator.

  $=\frac{3t-12-\left(2t-12\right)}{6t}$

  $\begin{array}{l}=\frac{3t-12-2t+12}{6t}\\ =\frac{t}{6t}\end{array}$

  $=\frac{1}{6}$

Conclusion:

Therefore, after simplification, the answer is $\frac{1}{6}$ .