What is 3/(x^2+y^2)+2/((x+y)^2) ?

The solution to 3/(x^2+y^2)+2/((x+y)^2) is (5x^2+6xy+5y^2)/((x+y)^2(x^2+y^2))

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simplify 3/(x^2+y^2)+2/((x+y)^2)

simplify

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

\frac{5 x ^{2} + 6 x y + 5 y ^{2}}{( x + y ) ^{2} ( x ^{2} + y ^{2} )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

3 (x + y)^{2} + 2 (x^{2} + y^{2}) : 5 x^{2} + 6 x y + 5 y^{2}

= \frac{5 x ^{2} + 6 x y + 5 y ^{2}}{( x + y ) ^{2} ( x ^{2} + y ^{2} )}

2 \cdot ∣ x ∣ = 9

- x = - 4

5^{2} + 2^{2}

7 \leq 3 y < 15

\frac{12 c ^{9}}{( 4 c ) ^{4}}

What is 3/(x^2+y^2)+2/((x+y)^2) ?
The solution to 3/(x^2+y^2)+2/((x+y)^2) is (5x^2+6xy+5y^2)/((x+y)^2(x^2+y^2))