what is the common denominator of $\frac{1}{a}+\frac{1}{b}$ in the complex fraction $\frac{\frac{1}{a}-\frac{…

what is the common denominator of $\frac{1}{a}+\frac{1}{b}$ in the complex fraction $\frac{\frac{1}{a}-\frac{1}{b}}{\frac{1}{a}+\frac{1}{b}}$?\n$a^{2}b^{2}$\n$a - b$\n$a + b$\n$ab$

what is the common denominator of $\frac{1}{a}+\frac{1}{b}$ in the complex fraction $\frac{\frac{1}{a}-\frac{1}{b}}{\frac{1}{a}+\frac{1}{b}}$?\n$a^{2}b^{2}$\n$a - b$\n$a + b$\n$ab$

Answer

Answer:

D. $ab$

Explanation:

Step1: Recall fraction addition rule

To add $\frac{1}{a}+\frac{1}{b}$, we use $\frac{m}{n}+\frac{p}{q}=\frac{mq + np}{nq}$.

Step2: Find common - denominator

For $\frac{1}{a}+\frac{1}{b}$, the common denominator of two fractions with denominators $a$ and $b$ is the least - common multiple of $a$ and $b$. Since $a$ and $b$ are variables (assuming they are non - zero), the least - common multiple of $a$ and $b$ is $ab$. We rewrite the fractions as $\frac{b}{ab}+\frac{a}{ab}=\frac{a + b}{ab}$. So the common denominator of $\frac{1}{a}+\frac{1}{b}$ is $ab$.