After you have $\dfrac{45}{a} + \dfrac{15}{c}$ on one side, factor out a common number and then combine the two fractions using a common denominator.

Once you have an equation of the form $\dfrac{30}{b} =$ (some fraction in $a$ and $c$), multiply by $b$ and by the other denominator so that you get a simple equation with no fractions.

When you reach an equation like something times $b$ equals something in $a$ and $c$, divide both sides by the coefficient of $b$ to express $b$ in terms of $a$ and $c$.

Choose simple positive numbers for $a$ and $c$, such as $a=3$ and $c=5$. In Desmos, type a=3 and c=5 to define them.

Enter the equation 45/a = 30/b - 15/c in Desmos. Then add a slider for b if prompted, and adjust it until the left-hand side and right-hand side values match (or use Desmos’s solve feature if available) to find the numerical value of $b$ for your chosen $a$ and $c$.

For each option, type its expression into Desmos using the same $a$ and $c$ values (for example, ac/(3c+a), (2ac)/(3c+a), etc.). Compare the numerical outputs of these expressions with the numerical value of $b$ you found from the original equation.

The correct answer choice is the one whose expression evaluates to the same numerical value as $b$ from the original equation. The others will give different numerical values.

Start with the given equation:

Add $\dfrac{15}{c}$ to both sides to move it away from the $b$ term:

Now the right side has only the $b$ term, which is what we want to solve for.

Factor out $15$ from the left-hand side:

Now combine $\dfrac{3}{a}$ and $\dfrac{1}{c}$ using the common denominator $ac$:

So the equation becomes

Simplify the right-hand side of

Multiply numerator and denominator on the right:

Now clear denominators by multiplying both sides by $b$ and then by $ac$:

• Multiply both sides by $b$:

• Then multiply both sides by $ac$:

Finally, divide both sides by $15$ to simplify:

This is now a simple linear equation in $b$. The last step is to isolate $b$.

From

divide both sides by $(3c + a)$ to solve for $b$:

This matches answer choice B.