if a^2-b^2=2ab, what is the value of (a+b)/(a-b)

We are given the equation \( a^2 - b^2 = 2ab \), and we want to find the value of \( \frac{a+b}{a-b} \).

### Step 1: Use the difference of squares identity
The left-hand side of the equation is a difference of squares, which can be factored as:
\[
a^2 - b^2 = (a + b)(a - b)
\]
So, the equation becomes:
\[
(a + b)(a - b) = 2ab
\]

### Step 2: Solve for \( \frac{a+b}{a-b} \)
Now divide both sides of the equation by \( (a - b) \) (assuming \( a \neq b \)) to isolate \( a + b \):
\[
a + b = \frac{2ab}{a - b}
\]
Finally, divide both sides by \( a - b \) to find \( \frac{a+b}{a-b} \):
\[
\frac{a+b}{a-b} = \frac{2ab}{(a-b)^2}
\]

Thus, the value of \( \frac{a+b}{a-b} \) is \( \frac{2ab}{(a-b)^2} \).

Would you like further details or clarifications?

Here are some related questions to explore:
1. How does the solution change if \( a = b \)?
2. Can this problem be solved geometrically or graphically?
3. How would this equation change if \( a^2 - b^2 = 3ab \) instead?
4. What would happen if \( b = 0 \) in this equation?
5. Can we express \( a + b \) in terms of other variables from this equation?

**Tip:** When dealing with factorizations like difference of squares, always check if the equation can be simplified further!

if a^2 - b^2 = 2ab, what is the value of (a+b)/(a-b)

Discover how to solve the equation a^2 - b^2 = 2ab and find the value of (a+b)/(a-b) using the difference of squares identity. This problem involves key algebraic concepts like factoring and simplifying equations. Suitable for students in Grades 9-11.

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