What is (x^2-y^2)/(x^2+2xy+y^2) ?

The solution to (x^2-y^2)/(x^2+2xy+y^2) is (x-y)/(x+y)

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simplify (x^2-y^2)/(x^2+2xy+y^2)

simplify

\frac{x ^{2} - y ^{2}}{x ^{2} + 2 x y + y ^{2}}

\frac{x - y}{x + y}

Solution steps

\frac{x ^{2} - y ^{2}}{x ^{2} + 2 x y + y ^{2}}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

x^{2} - y^{2} = (x + y) (x - y)

= \frac{( x + y ) ( x - y )}{x ^{2} + 2 x y + y ^{2}}

Apply Perfect Square Formula:

a^{2} + 2 ab + b^{2} = (a + b)^{2}

x^{2} + 2 x y + y^{2} = (x + y)^{2}

= \frac{( x + y ) ( x - y )}{( x + y ) ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x + y)^{2} = (x + y) (x + y)

= \frac{( x + y ) ( x - y )}{( x + y ) ( x + y )}

Cancel the common factor:

x + y

= \frac{x - y}{x + y}

\frac{x - 2}{x - 6} > 0

10 + 4 x = 5 (x - 6) + 33

x - 6 \geq 2

- 5 - 9 b \leq 4 - 6 b

\frac{4}{7} = \frac{x}{6}

What is (x^2-y^2)/(x^2+2xy+y^2) ?
The solution to (x^2-y^2)/(x^2+2xy+y^2) is (x-y)/(x+y)