What is (1+x-y)/(1+x+y)+(1+x+y)/(1+x-y) ?

The solution to (1+x-y)/(1+x+y)+(1+x+y)/(1+x-y) is (2x^2+4x+2y^2+2)/((x+y+1)(x+1-y))

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simplify (1+x-y)/(1+x+y)+(1+x+y)/(1+x-y)

simplify

\frac{1 + x - y}{1 + x + y} + \frac{1 + x + y}{1 + x - y}

\frac{2 x ^{2} + 4 x + 2 y ^{2} + 2}{( x + y + 1 ) ( x + 1 - y )}

Solution steps

\frac{1 + x - y}{1 + x + y} + \frac{1 + x + y}{1 + x - y}

Least Common Multiplier of

1 + x + y, 1 + x - y : (x + y + 1) (x + 1 - y)

Adjust Fractions based on the LCM

= \frac{( 1 + x - y ) ^{2}}{( x + y + 1 ) ( x + 1 - y )} + \frac{( 1 + x + y ) ^{2}}{( x + y + 1 ) ( x + 1 - y )}

Apply the fraction rule:

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

= \frac{( 1 + x - y ) ^{2} + ( 1 + x + y ) ^{2}}{( x + y + 1 ) ( x + 1 - y )}

Simplify

(1 + x - y)^{2} + (1 + x + y)^{2} : 2 x^{2} + 4 x + 2 y^{2} + 2

= \frac{2 x ^{2} + 4 x + 2 y ^{2} + 2}{( x + y + 1 ) ( x + 1 - y )}

\frac{5}{x} \cdot \frac{2 x}{y ^{2}} \cdot \frac{3 y}{10}

8 + \frac{x - 1}{x + 4}

lo g_{10} (x^{2} - 9) - lo g_{10} (x^{2} + 6 x + 9)

\frac{144}{81}

2 \cdot 19

What is (1+x-y)/(1+x+y)+(1+x+y)/(1+x-y) ?
The solution to (1+x-y)/(1+x+y)+(1+x+y)/(1+x-y) is (2x^2+4x+2y^2+2)/((x+y+1)(x+1-y))