What is ((x^p))/((x^p+x^q))+1/((x^{p-q)+1)} ?

The solution to ((x^p))/((x^p+x^q))+1/((x^{p-q)+1)} is (x^{-q+2p}+2x^p+x^q)/((x^{-q+p)+1)(x^p+x^q)}

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simplify ((x^p))/((x^p+x^q))+1/((x^{p-q)+1)}

simplify

\frac{( x ^{p} )}{( x ^{p} + x ^{q} )} + \frac{1}{( x ^{p - q} + 1 )}

\frac{x ^{- q + 2 p} + 2 x ^{p} + x ^{q}}{( x ^{- q + p} + 1 ) ( x ^{p} + x ^{q} )}

Solution steps

\frac{x ^{p}}{x ^{p} + x ^{q}} + \frac{1}{x ^{p - q} + 1}

Least Common Multiplier of

x^{p} + x^{q}, x^{p - q} + 1 : (x^{- q + p} + 1) (x^{p} + x^{q})

Adjust Fractions based on the LCM

= \frac{x ^{p} ( x ^{- q + p} + 1 )}{( x ^{- q + p} + 1 ) ( x ^{p} + x ^{q} )} + \frac{x ^{p} + x ^{q}}{( x ^{- q + p} + 1 ) ( x ^{p} + x ^{q} )}

Apply the fraction rule:

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

= \frac{x ^{p} ( x ^{- q + p} + 1 ) + x ^{p} + x ^{q}}{( x ^{- q + p} + 1 ) ( x ^{p} + x ^{q} )}

Simplify

x^{p} (x^{- q + p} + 1) + x^{p} + x^{q} : x^{- q + 2 p} + 2 x^{p} + x^{q}

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

(32 - x) + x + (25 - x) + 12

(\frac{a}{2} + \frac{b}{5})^{3}

(x + 3)^{3} - (x - 1)^{3}

- 4 x + (- 6) x

(x - 3 x)^{2} - a (x^{2} - 3 x) - 20

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