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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

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

Solution steps

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

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}

6 \times 1 0^{- 2}

\frac{\frac{77}{9}}{2.5}

38

2 x - 9 x

\frac{3}{2} \cdot (- 4)

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