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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{5bc}{3} - \frac{5}{b}$

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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{5bc}{3} - \frac{5}{b}

Identify LCM of Denominators: Identify the least common multiple (LCM) of the denominators $3$ and $b$ . Since $3$ and $b$ are not like terms and assuming $b$ is not a multiple of $3$ , the LCM is $3b$ .
Make Denominators the Same: Make the denominators the same by multiplying the first fraction by $\frac{b}{b}$ and the second fraction by $\frac{3}{3}$ . This gives us $\frac{(5bc \cdot b)}{(3 \cdot b)} - \frac{(5 \cdot 3)}{(b \cdot 3)}$ .
Perform Multiplications: Perform the multiplications in the numerators and denominators. This results in $(\frac{5b^2c}{3b}) - (\frac{15}{3b})$ .
Combine Fractions: Combine the fractions by subtracting the numerators since the denominators are the same. The combined fraction is $\frac{(5b^2c) - 15}{3b}$ .
Check for Simplification: Check if the numerator can be simplified further. In this case, there are no common factors between $5b^2c$ and $15$ that would allow us to simplify the fraction further, assuming $c$ is not a multiple of $3$ .

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