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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

x^{2} - 1 - 2 a - a^{2}

a^{12} + a^{8} - a^{4} - 1

x^{6} - 7 x^{2} - 6

\frac{( 9 a ^{6} b ^{10} )}{( 3 a ^{2} b ^{5} )}

8 h^{6} - 27 j^{9}

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