Question

Simplify the expression. $$\frac{42 t}{-14 z} \div \frac{-6}{7 t}$$

Short answer

The simplified form of the expression is \( \frac{7 t^2}{2 z} \)

Step-by-step solution

Arrangement

Firstly, rearrange the given expression as a multiplication problem where the second fraction flips (reciprocal) and changes the division to multiplication.So, \(\frac{42 t}{-14 z} \div \frac{-6}{7 t}\) becomes \(\frac{42 t}{-14 z} * \frac{7 t}{-6}\)

Perform Multiplication

Next, perform the multiplication across the numerators and the denominators separately.So, \(\frac{42 t}{-14 z} * \frac{7 t}{-6}\) becomes \(\frac{42 t * 7 t}{-14 z * -6}\)

Simplify Multiplication

Simplify the terms in both the numerator and the denominator to obtain \(\frac{294 t^2}{84 z}\)

Simplify the fraction

Reduce the fraction to its simplest form by dividing both numerator and denominator by their greatest common divisor, which is 42. Thus, \(\frac{294 t^2}{84 z}\) simplifies further to \(\frac{7 t^2}{2 z}\)