✅ Excellent! You got it! 😀 Here's the next question: What is the simplest form of the following expression?…

Question

✅ Excellent! You got it! 😀 Here's the next question: What is the simplest form of the following expression? (8y − 9b)/9 + 9y/2 A: (7y − 18b)/2 B: (−73y − 81b)/9 C: (17y − 9b)/18 D: (97y − 18b)/18

ScanSolve AI Tutor · Accepted Answer

To simplify the expression, we need to find a common denominator for the two fractions.

Find the least common multiple (LCM) of the denominators 9 and 2.
The LCM of 9 and 2 is 18.
Rewrite each fraction with the common denominator 18.
$\frac{8y - 9b}{9} = \frac{(8y - 9b) \times 2}{9 \times 2} = \frac{16y - 18b}{18}$ $\frac{9y}{2} = \frac{9y \times 9}{2 \times 9} = \frac{81y}{18}$
Add the two fractions.
$\frac{16y - 18b}{18} + \frac{81y}{18} = \frac{16y - 18b + 81y}{18}$
Combine the like terms in the numerator.
$\frac{(16y + 81y) - 18b}{18} = \frac{97y - 18b}{18}$
The simplest form of the expression is $\frac{97y - 18b}{18}$ .

Comparing this with the given options, it matches option D.

The final answer is $\text{D: } \frac{97y - 18b}{18}$ .

✅ Excellent! You got it! 😀 Here's the next question: What is the simplest form of the following expression? (8y - 9b)/9 + 9y/2 A: (7y - 18b)/2 B: (-73y - 81b)/9 C: (17y - 9b)/18 D: (97y - 18b)/18

Answer

Step-by-step solution

Find the least common multiple (LCM) of the denominators 9 and 2.

Rewrite each fraction with the common denominator 18.

Add the two fractions.

Combine the like terms in the numerator.

Try one yourself

Still stuck on this one?

More Mathematics Questions