Add or subtract as indicated and simplify if possible.
\[
\frac{1}{6 y^{2}}+\frac{-7}{8 y}
\]
Select one:
a. $\frac{-6}{48 y^{3}}$
b. $\frac{-21 y+4}{24 y^{2}}$
C. $\frac{-17}{24 y^{2}}$
d. $\frac{6}{14 y^{3}}$
Answer
Final Answer: \(\boxed{\frac{-21y+4}{24y^2}}\) which corresponds to option b.
Step 1 ：The problem is asking to add two fractions: \(\frac{1}{6y^2}\) and \(\frac{-7}{8y}\).
Step 2 ：Since the fractions do not have the same denominator, we need to find a common denominator. The least common denominator (LCD) of \(6y^2\) and \(8y\) is \(24y^2\).
Step 3 ：We rewrite the fractions with the LCD: \(\frac{1}{6y^2}\) becomes \(\frac{4}{24y^2}\) and \(\frac{-7}{8y}\) becomes \(\frac{-21y}{24y^2}\).
Step 4 ：Adding the fractions gives us \(\frac{4-21y}{24y^2}\) which simplifies to \(\frac{-21y+4}{24y^2}\).
Step 5 ：Final Answer: \(\boxed{\frac{-21y+4}{24y^2}}\) which corresponds to option b.
