Question

hw 12.2_add & subtract rational expressions
score: 9/17 answered: 9/17
question 10
simplify and reduce to the lowest terms. (leave answer in factored form.)
\\(\frac{8}{x} - \frac{13}{y} = \\)

Explanation:

Step1: Find common denominator

The common denominator of $x$ and $y$ is $xy$. Rewrite each fraction with this denominator:
$\frac{8}{x} = \frac{8y}{xy}$, $\frac{13}{y} = \frac{13x}{xy}$

Step2: Subtract the fractions

Subtract the numerators over the common denominator:
$\frac{8y}{xy} - \frac{13x}{xy} = \frac{8y - 13x}{xy}$

Step3: Verify lowest terms

The numerator $8y-13x$ has no common factors with the denominator $xy$, so the expression is in lowest terms.

Answer:

$\frac{8y - 13x}{xy}$