Question

module 7 pretest: rational expressions and equations
module 7 pretest: rational expressions and equations
score: 3/9 answered: 3/9
question 4
subtract \\(\frac{10x + 2}{x + 5} - \frac{4x + 3}{x + 5} = \\) and state the difference in simplest form.
the domain is \\(x \
eq \\)

Explanation:

Step1: Subtract the numerators

Since the denominators are the same ($x + 5$), we subtract the numerators: $(10x + 2) - (4x + 3)$.
Calculating the numerator: $10x + 2 - 4x - 3 = 6x - 1$.
So the rational expression becomes $\frac{6x - 1}{x + 5}$.

Step2: Find the domain restriction

The denominator of a rational expression cannot be zero. So we set $x + 5 = 0$.
Solving for $x$: $x = -5$. Thus, $x
eq -5$.

Answer:

The simplified difference is $\frac{6x - 1}{x + 5}$ and the domain is $x
eq -5$.