Consider how multiplying or dividing the given values could lead to the desired result.
Example Solution: \text{-}\dfrac {3yz}{2x}
Practice makes perfect
There are many expressions we can create with the given values of x, y, and z to obtain a result of 1. We have that x= -3, y= -2, and z= -1. For our expression, we will arbitrarily choose to create a fraction. Now, for example, we can let the numerator of the fraction be 3yz.
3yz= 3( - 2)( - 1) = 6
From here, we can think about what we might divide 6 by to end with 1. Since the result needs to be positive, the number we are looking for is positive. The result also is a whole number. Consider a few possibilities.
Possible Number
Division
Result
1
6 ÷ 1
6
2
6 ÷ 2
3
3
6 ÷ 3
2
6
6 ÷ 6
1
That means that the denominator of our fraction must be 6. Notice that if we multiply -2 by x we will obtain exactly 6.
-2 * x =- 2( - 3) = 6
Knowing that, we can complete our expression.
\begin{gathered}
\dfrac {3yz}{\text{-}2x} \quad \Leftrightarrow \quad \text{-}\dfrac{3yz}{2x}
\end{gathered}
We can verify that this works by substituting the given values into our expression.
