Question

subtract.
\\(\frac{5y - 3}{3y} - \frac{4y + 1}{5y}\\)
simplify your answer as much as possible.

Explanation:

Step1: Find a common denominator

The denominators are \(3y\) and \(5y\), so the common denominator is \(15y\).
Rewrite each fraction with the common denominator:
\(\frac{5y - 3}{3y}=\frac{(5y - 3)\times5}{3y\times5}=\frac{25y - 15}{15y}\)
\(\frac{4y + 1}{5y}=\frac{(4y + 1)\times3}{5y\times3}=\frac{12y + 3}{15y}\)

Step2: Subtract the fractions

Subtract the numerators while keeping the common denominator:
\(\frac{25y - 15}{15y}-\frac{12y + 3}{15y}=\frac{(25y - 15)-(12y + 3)}{15y}\)

Step3: Simplify the numerator

Expand and combine like terms in the numerator:
\((25y - 15)-(12y + 3)=25y - 15 - 12y - 3 = 13y - 18\)

Step4: Write the final fraction

So the result is \(\frac{13y - 18}{15y}\)

Answer:

\(\frac{13y - 18}{15y}\)