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)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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 )}

(\frac{3}{x + 4 x}) (\frac{- 2 x - 7}{x})

3 x^{2.5} \cdot 3 x^{2.5} \cdot 3 x^{2.5} \cdot 3 x^{2.5}

l^{- 1} [\frac{10}{( s + 6 ) ^{6}}]

5 (- a^{3} b^{2} c)^{3}

- 512 (x^{1})^{7} + 64 x^{8}

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)}