Question

Simplify the expression. $$\frac{9 x^{2}}{4} \cdot \frac{8}{18 x}$$

Short answer

The expression simplifies to \(\ x\).

Step-by-step solution

Break Apart Fractions

To simplify this expression, one is advised to deal with the numbers and the variables separately. Therefore, \(9x^{2}\over 4\) can be separated to \(9/4\) * \(x^{2}\) and \({8/18x}\) can be separated to \(8/18\) * \(1/x\)

Simplify Numerical Fractions

\(9/4\) remains as it is since 9 is not divisible by 4. However, \(8/18\) reduces to \(4/9\) when both top and bottom are divided by 2.

Simplify Variable Components

Multiplying terms with the same bases (i.e., x's) by adding exponents. So, \(x^{2}\) * \(1/x\) simplifies to \(1/x\). This is because when you divide with the same base, you subtract the bottom exponent from the top one. In effect, \(2-1=1\).

Multiply Constants and Variables

Multiply the constants together and the variables together. This gives us: \(9/4\) * \(4/9\) * \(x\), simplifying this leads to a cancellation of \(9/4\) and \(4/9\) to yield an x.

Final Answer

After simplification, the expression reduces to \(x\)