Question

(x^2+2xy+y^2)÷(a^2-b^2)÷(x+y)÷(a+b)

Answer 1

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Answer 2

To simplify the expression:

1. Factor the numerator:
   $x^2 + 2xy + y^2 = (x + y)^2$.

2. Factor the denominator:
   $a^2 - b^2 = (a + b)(a - b)$.

Now, let's simplify the expression:

$\frac{{(x^2 + 2xy + y^2)}}{{(a^2 - b^2)}} \div \frac{{(x + y)}}{{(a + b)}}$

Substituting the factored forms:

$\frac{{(x + y)^2}}{{(a + b)(a - b)}} \div \frac{{(x + y)}}{{(a + b)}}$

Since we're dividing by a fraction, we can multiply by its reciprocal:

$\frac{{(x + y)^2}}{{(a + b)(a - b)}} \cdot \frac{{(a + b)}}{{(x + y)}}$

Now, we can cancel out the common factors in the numerator and denominator:

$\frac{{(x + y) \cdot (x + y)}}{{(a + b) \cdot (a - b)}}$

Simplifying further, we have:

$\frac{{(x + y)^2}}{{(a + b)(a - b)}}$

Therefore, the simplified expression is $(x + y)^2$ divided by $(a + b)(a - b)$.