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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{4}{y^5} - \frac{z^4}{2}$

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Add and subtract rational expressions

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{4}{y^5} - \frac{z^4}{2}

Find LCM: Find the least common multiple (LCM) of the denominators $y^5$ and $2$ . Since $y^5$ and $2$ have no common factors other than $1$ , the LCM is simply the product of the two, which is $2y^5$ .
Make denominators same: Make the denominators the same by multiplying the first fraction by $\frac{2}{2}$ and the second fraction by $\frac{y^5}{y^5}$ . This gives us $\frac{4\times 2}{y^5\times 2} - \frac{z^4\times y^5}{2\times y^5}$ .
Perform multiplications: Perform the multiplications in the numerators and denominators. This results in $\frac{8}{y^5} - \frac{z^4y^5}{2y^5}.$
Combine fractions: Since the denominators are now the same, we can combine the fractions. This gives us $(8 - z^4y^5)/2y^5$ .
Check for simplification: Check if the expression can be simplified further. Since $8$ and $z^4y^5$ have no common factors, and the denominator $2y^5$ is already in simplest form, the expression cannot be simplified further.

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