Q20. - Algebra 1

Question

Simplify each expression.

$\frac{\mathbf{2}\mathbf{x}{\mathbf{y}}^2}{\mathbf{16}\mathbf{x}\mathbf{y}\mathbf{z}}$

Step-by-Step Solution

Answer

The given expression can be simplified to $\frac{\mathbf{y}}{\mathbf{8}\mathbf{z}}$.

Step 1. Simplify rational function.

Let $x,y$, and $z$, be polynomials with $x\ne 0$ and $z\ne 0$.

$\frac{yx}{zx}=\frac{y\cdot x}{z\cdot x}=\frac{y}{z}$

Step 2. Factor.

Factor each number and write all powers of variables as products.

$\frac{2\cdot x\cdot y\cdot y}{2\cdot 2\cdot 2\cdot 2\cdot x\cdot y\cdot z}$

Step 3. Divide.

Divide out common factors.

$\frac{y}{2\cdot 2\cdot 2\cdot z}=\frac{y}{8z}$

Therefore, the given expression can be simplified to $\frac{y}{8z}$.