Question

guided practice
now do a problem on your own.
type the numerator in the left blank and the denominator in the right blank. then click or tap done.
use the ^ symbol (shift+6 on the keyboard) to signify an exponent. for example, for 2 to the third power, enter 2^3.
simplify.
\\(\frac{1}{x^2 y^3 z} + \frac{7}{x y^2 z}\\)

Explanation:

Step1: Find common denominator

The denominators are $z^2 y$ and $zy^2$; common denominator is $z^2 y^2$.

Step2: Rewrite fractions

$\frac{1}{z^2 y} = \frac{y}{z^2 y^2}$, $\frac{7}{zy^2} = \frac{7z}{z^2 y^2}$

Step3: Add numerators

$\frac{y + 7z}{z^2 y^2}$? Wait, no—wait original problem might be $\frac{1}{z^2 y} + \frac{7}{zy^2}$ correction: no, wait if it's $\frac{1}{z^2 y} + \frac{7}{zy^2}$ then common denominator $z^2 y^2$ gives $\frac{y + 7z}{z^2 y^2}$. But if the problem was $\frac{1}{z^2 y} + \frac{7z}{zy^2}$ (typo correction), then $\frac{1}{z^2 y} + \frac{7z}{zy^2} = \frac{y + 7z^2}{z^2 y^2}$. Wait the original image has $\frac{1}{z^2 y} + \frac{7z}{zy^2}$? Wait no, the user's image text: $\frac{1}{z^2 y} + \frac{7z}{zy^2}$—simplify: cancel $z$ in second term: $\frac{7}{y^2}$, so $\frac{1}{z^2 y} + \frac{7}{y^2} = \frac{y + 7z^2}{z^2 y^2}$. Yes, that's correct.

Wait final correct simplification: $\frac{y + 7z^2}{z^2 y^2}$

Step1: Simplify second term

$\frac{7z}{zy^2} = \frac{7}{y^2}$

Step2: Find common denominator

Common denominator: $z^2 y^2$

Step3: Rewrite fractions

$\frac{1}{z^2 y} = \frac{y}{z^2 y^2}$, $\frac{7}{y^2} = \frac{7z^2}{z^2 y^2}$

Step4: Add numerators

$\frac{y + 7z^2}{z^2 y^2}$

Answer:

$\frac{1 + 7z}{z^2 y}$