What is 1/((1+a^{y-x))}+1/((1+a^{x-y))} ?

The solution to 1/((1+a^{y-x))}+1/((1+a^{x-y))} is (a^{x-y}+a^{y-x}+2)/((a^{y-x)+1)(a^{x-y}+1)}

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simplify 1/((1+a^{y-x))}+1/((1+a^{x-y))}

simplify

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

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

Solution steps

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

Least Common Multiplier of

1 + a^{y - x}, 1 + a^{x - y} : (a^{y - x} + 1) (a^{x - y} + 1)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

a^{x - y} + 1 + a^{y - x} + 1 : a^{x - y} + a^{y - x} + 2

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

\frac{b \cdot ( 2 \frac{a}{36} ) ^{3}}{( 4 \frac{a}{b} ) ^{2}}

(- 1 x^{2} - 3) - (- 1.1)

(\frac{2}{x - 1})^{3} - (\frac{2}{x - 1})^{2} - 2 (\frac{2}{x - 1}) - 1

2 x^{3} - x^{2} + 9 x + 5

(100 - q)^{3}

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