What is ((x+y)^2)/(x^4-y^4) ?

The solution to ((x+y)^2)/(x^4-y^4) is (x+y)/((x^2+y^2)(x-y))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((x+y)^2)/(x^4-y^4)

simplify

\frac{( x + y ) ^{2}}{x ^{4} - y ^{4}}

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

Solution steps

\frac{( x + y ) ^{2}}{x ^{4} - y ^{4}}

x^{4} = (x^{2})^{2}

y^{4} = (y^{2})^{2}

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

Apply Difference of Two Squares Formula:

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

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

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

Cancel the common factor:

x + y

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

\frac{3}{2} - 2^{2} + 3.5

3 5^{2}

10 x^{2} + 23 x - 5

\frac{( 12 x + 4 )}{\frac{2}{3}}

- (1^{2})

What is ((x+y)^2)/(x^4-y^4) ?
The solution to ((x+y)^2)/(x^4-y^4) is (x+y)/((x^2+y^2)(x-y))