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

The solution to (4xy)/(x^2-y^2)+(x-y)/(x+y) is (x^3+3xy^2+y^3+3x^2y)/((x+y)(x^2-y^2))

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

simplify

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

\frac{x ^{3} + 3 x y ^{2} + y ^{3} + 3 x ^{2} y}{( x + y ) ( x ^{2} - y ^{2} )}

Solution steps

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

Least Common Multiplier of

x^{2} - y^{2}, x + y : (x + y) (x^{2} - y^{2})

Adjust Fractions based on the LCM

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

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

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

Simplify

4 x y (x + y) + (x - y) (x^{2} - y^{2}) : x^{3} + 3 x y^{2} + y^{3} + 3 x^{2} y

= \frac{x ^{3} + 3 x y ^{2} + y ^{3} + 3 x ^{2} y}{( x + y ) ( x ^{2} - y ^{2} )}

4 x - 3 > 2 x + 7

3 r^{2} + 5 r - 2

6 x^{2} + 13 x + 5

\frac{x ^{2}}{4} < 1

∣ a ∣ = 3

What is (4xy)/(x^2-y^2)+(x-y)/(x+y) ?
The solution to (4xy)/(x^2-y^2)+(x-y)/(x+y) is (x^3+3xy^2+y^3+3x^2y)/((x+y)(x^2-y^2))