Question: Question 18, 6.2.65 Subtract the rational expressions. \frac{20x + 3}{6x + 7} - \frac{-10x -…

Question 18, 6.2.65

Subtract the rational expressions.

\frac{20x + 3}{6x + 7} - \frac{-10x - 32}{6x + 7}

\frac{20x + 3}{6x + 7} - \frac{-10x - 32}{6x + 7} = □ (Simplify your answer.)

Solution

Step 1

\[ \frac{20x + 3}{6x + 7} - \frac{-10x - 32}{6x + 7} \]

Step 2

Combine the numerators since the denominators are the same.

\[ \frac{20x + 3 - (-10x - 32)}{6x + 7} \]

Step 3

Simplify the numerator.

\[ 20x + 3 + 10x + 32 = 30x + 35 \]

Step 4

The expression becomes:

\[ \frac{30x + 35}{6x + 7} \]

Step 5

Factor the numerator.

\[ \frac{5(6x + 7)}{6x + 7} \]

Step 6

Cancel the common factor.

\[ 5 \]

Answer:
5