What is ((x+1))/((sqrt(x^2-1))) ?

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

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simplify ((x+1))/((sqrt(x^2-1)))

simplify

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

\frac{x ^{2} - 1}{x - 1}

Solution steps

\frac{x + 1}{x ^{2} - 1}

Multiply by the conjugate

\frac{x ^{2} - 1}{x ^{2} - 1}

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

x^{2} - 1 x^{2} - 1 = x^{2} - 1

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

Factor

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

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

Cancel the common factor:

x + 1

= \frac{x ^{2} - 1}{x - 1}

x^{5} - 3 x^{7} + 2 x

100 x^{2} - 25 y^{2}

\frac{7}{9} x + \frac{4}{3} x

\frac{( 2 \cdot 2 ^{n} - 2 \cdot 2 ^{n - 2} )}{( 2 ^{n} - 2 ^{n - 1} )}

lo g_{2} (g) (\frac{1}{8})

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