What is (3x+1)/(x-1)+x/(x^2-1) ?

The solution to (3x+1)/(x-1)+x/(x^2-1) is (3x^2+5x+1)/((x-1)(x+1))

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simplify (3x+1)/(x-1)+x/(x^2-1)

simplify

\frac{3 x + 1}{x - 1} + \frac{x}{x ^{2} - 1}

\frac{3 x ^{2} + 5 x + 1}{( x - 1 ) ( x + 1 )}

Solution steps

\frac{3 x + 1}{x - 1} + \frac{x}{x ^{2} - 1}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{( 3 x + 1 ) ( x + 1 )}{( x - 1 ) ( x + 1 )} + \frac{x}{( x - 1 ) ( x + 1 )}

Apply the fraction rule:

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

= \frac{( 3 x + 1 ) ( x + 1 ) + x}{( x - 1 ) ( x + 1 )}

Simplify

(3 x + 1) (x + 1) + x : 3 x^{2} + 5 x + 1

= \frac{3 x ^{2} + 5 x + 1}{( x - 1 ) ( x + 1 )}

\frac{x ^{2} + 3 x - 18}{7 x - 21}

\frac{7 + 23 i}{- 3 - 5 i}

(2 a + 3)^{2}

(y - 9)^{2}

(- 7 - 9 i) + (- 6 - 7 i)

What is (3x+1)/(x-1)+x/(x^2-1) ?
The solution to (3x+1)/(x-1)+x/(x^2-1) is (3x^2+5x+1)/((x-1)(x+1))