https://file.aiquickdraw.com/mathbot/file/1725531553517ktwzgxd4.jpg

The equation in the image is:

\[
\frac{12}{y - 3} = \frac{15}{y + 3}
\]

To solve for \( y \), we can cross-multiply:

\[
12(y + 3) = 15(y - 3)
\]

Now, distribute on both sides:

\[
12y + 36 = 15y - 45
\]

Next, get all terms involving \( y \) on one side by subtracting \( 12y \) from both sides:

\[
36 = 3y - 45
\]

Now add \( 45 \) to both sides:

\[
81 = 3y
\]

Finally, divide by \( 3 \):

\[
y = 27
\]

So, the value of \( y \) is \( 27 \).

Would you like further explanation or details on any step? Here are five related questions you might find helpful:

1. How do you verify the solution for \( y \)?
2. What are cross-multiplication steps in solving fractions?
3. Can this equation have any other solutions?
4. How do we simplify or expand terms in equations like this?
5. What other methods can solve this type of equation?

**Tip:** When solving equations with fractions, cross-multiplication is a useful method if you have one fraction on each side of the equation.

What is the value of y in 12/(y - 3) = 15/(y + 3)?

Learn how to solve the equation 12/(y - 3) = 15/(y + 3) using cross-multiplication. The solution involves basic algebraic techniques to isolate and solve for y. Suitable for students in Grades 7-10.

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