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Simplify. Write your answer using whole numbers and variables. $\newline$ $\frac{z}{5z^2 - 6z}$

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Simplify radical expressions: mixed review

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Q. Simplify. Write your answer using whole numbers and variables.

\newline

\frac{z}{5z^2 - 6z}

Simplify Fraction: Simplify the expression $\frac{z}{5z^2} - 6z$ by combining like terms. $\newline$ First, we need to simplify the fraction $\frac{z}{5z^2}$ . To do this, we can cancel out a $z$ from the numerator and denominator. $\newline$ $\frac{z}{5z^2} = \frac{1}{5z}$ $\newline$ Now, we have $\frac{1}{5z} - 6z$ .
Find Common Denominator: Find a common denominator to combine the terms. $\newline$ Since $\frac{1}{5z}$ and $6z$ do not have the same denominator, we need to find a common denominator to combine them. The common denominator is $5z$ . $\newline$ $\frac{1}{5z} - 6z = \frac{1}{5z} - \frac{(6z \cdot 5z)}{5z}$
Perform Multiplication: Perform the multiplication in the second term. $\newline$ Now, we multiply $6z$ by $5z$ to get $30z^2$ . $\newline$ $\frac{1}{5z} - \frac{(6z \times 5z)}{5z} = \frac{1}{5z} - \frac{30z^2}{5z}$
Combine Terms: Combine the terms over the common denominator. $\newline$ Now that we have a common denominator, we can combine the terms. $\newline$ $\frac{1}{5z} - \frac{30z^2}{5z} = \frac{1 - 30z^2}{5z}$
Simplify Numerator: Simplify the numerator. $\newline$ We can't simplify $1 - 30z^2$ any further since they are not like terms. $\newline$ So, the final simplified expression is $(1 - 30z^2)/5z$ .

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